Sourav Patra

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Papers by Sourav Patra

A parameterization of parahermitian matrix functions and its application to a state-space solution for -analysis

Systems & Control Letters, 2011

In this paper, an economic parameterization for positive parahermitian matrix functions is introd... more In this paper, an economic parameterization for positive parahermitian matrix functions is introduced and applied to the µ-analysis framework wherein we propose a new state-space optimization problem for finding the required D-scales. Among the four state-space matrices to be used to realize the optimal D-scale, A and B are chosen via a Laguerre parameterization whereas the other two state-space matrices, C and D are obtained by spectral factorization after solving a convex optimization problem formulated in an LMI framework. The obtained D-scale satisfies the commuting property with the uncertainty structure. The proposed economic parameterization yields advantages in terms of less computational time and less number of decision variables and also, the proposed state-space optimization framework gives a frequency independent solution algorithm in state-space variables for the required D-scales. Two numerical examples are used to demonstrate the effectiveness of the proposed algorithm.

format_quotePresents dual objectives: a novel parameterization of parahermitian matrix functions and a state-space solution improving computational efficiency.format_quote

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Stability Analysis of Interconnected Systems With “Mixed” Negative-Imaginary and Small-Gain Properties

IEEE Transactions on Automatic Control, 2011

In this letter, an analytical framework is proposed to examine stability of two stable, linear ti... more In this letter, an analytical framework is proposed to examine stability of two stable, linear time invariant systems interconnected in positive feedback where the systems have "mixed" properties of negative-imaginary and small-gain. Using the notion of dissipativity, the interconnection of systems is guaranteed to be finite-gain stable under the condition that the dc loop gain is contractive. This work builds on Griggs, et al. [14] and exploits a new set of frequency dependent triplets that was introduced in above reference to "mix" two unconditional stability statements, i.e., small-gain and passivity. Unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative-imaginary systems are connected in a feedback loop can be "mixed" with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop. The usefulness of the proposed analytical framework is demonstrated via a numerical example.

format_quoteInternal stability for positive feedback interconnections relies on a contractive dc loop gain, introducing conditional stability concepts.format_quote

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Towards Controller Synthesis for Systems with Negative Imaginary Frequency Response

IEEE Transactions on Automatic Control, 2010

In this technical note, we introduce the concepts of sigma exponent of discrete linear time varyi... more In this technical note, we introduce the concepts of sigma exponent of discrete linear time varying system. It is shown that these exponents describe the possible changes in the Lyapunov exponents under perturbation decreasing at infinity at exponential rate. Finally we present formulas for the exponential exponents in terms of transition matrix of the system.

format_quoteNegative-imaginary systems in lightly damped flexible structures pose unique control challenges due to complex modal behavior.format_quote

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A Strongly Strict Negative-Imaginary Lemma for

Abstract. A state-space characterization is given for strongly strict negative-imaginary systems.... more Abstract. A state-space characterization is given for strongly strict negative-imaginary systems. It facilitates both robust analysis and synthesis methods for interconnected negative-imaginary systems. Numerical advantages are achieved by avoiding a non-convex rank constraint, a non-strict inequality condition and a minimality assumption present in previous literature. Key words: negative-imaginary systems, positive-real, non-minimal realization Notation. Notation is standard. R and RH ∞ denote the set of all proper realrational and proper real-rational stable transfer function matrices, respectively. R and C are the fields of real and complex numbers, respectively. The superscript (·) n×m denotes an operator with m columns and n rows. Re[s] and Im[s] denote the real and imaginary part of a complex number s ∈ C, respectively. Furthermore, let A ∗ be the complex conjugate transpose of matrix A, and let det(A) be the determinant of a square matrix A. 1. Introduction. Negative-imagina...

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State Feedback Controller Design for Discrete-Time Linear System with Time-Varying Delay Using a New Lyapunov-Krasovskii Functional

2018 15th IEEE India Council International Conference (INDICON)

This paper presents the stabilization problem of linear discrete-time systems with time-varying d... more This paper presents the stabilization problem of linear discrete-time systems with time-varying delay using a new Lyapunov-Krasovskii (LK) functional. A tighter estimate of the forward difference of LK functional is obtained by invoking the summation inequality and reciprocally convex combination lemma. A delay-dependent condition for the existence of state-feedback controller is derived in linear matrix inequality (LMI) framework which ensures asymptotic stability in the sense of Lyapunov. The effectiveness of the proposed results is demonstrated through numerical examples.

Observer-Based Stabilization of Linear Discrete Time-VaryingDelay Systems

Journal of Dynamic Systems, Measurement, and Control

This paper presents the design of an observer-based stabilizing controller for linear discrete-ti... more This paper presents the design of an observer-based stabilizing controller for linear discrete-time systems subject to interval time-varying state-delay. In this work, the problem has been formulated in convex optimization framework by constructing a new Lyapunov–Krasovskii (LK) functional to derive delay-dependent stabilization criteria. The summation inequality and the extended reciprocally convex inequality are exploited to obtain a less conservative delay upper bound in linear matrix inequality (LMI) framework. The derived stability conditions are delay-dependent and thus ensure global asymptotic stability in presence of any time-delay less than the obtained delay upper bound. Numerical examples are included to demonstrate the usefulness of the developed results.

Observer-based controller design for linear time-varying delay systems using a new Lyapunov-Krasovskii functional

International Journal of Automation and Control

This paper presents an observer-based controller design method for linear systems with interval t... more This paper presents an observer-based controller design method for linear systems with interval time-varying state-delay. In this work, using a new Lyapunov-Krasovskii (LK) functional, a less conservative stabilisation criterion is derived. The Wirtinger's inequality and reciprocally convex combination lemma are exploited to develop a computationally tractable method by representing the design constraints in linear matrix inequality (LMI) framework. Numerical examples are given to demonstrate the superiority of the proposed results over the existing method.

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Robust controller design method for linear systems with parametric uncertainty using minimum eigenvalue approach

IFAC-PapersOnLine

Abstract In this paper, a static state feedback robust controller design method for linear system... more Abstract In this paper, a static state feedback robust controller design method for linear systems with parametric uncertainty is presented. The closed-loop stability analysis is carried out in the sense of Lyapunov and the controller design parameters with constraints are formulated in linear matrix inequality (LMI) framework. A less conservative robust stability result is obtained by introducing a new set of sufficient conditions developed which contains the information of minimum eigenvalue of the perturbation matrices. The control effort is also reduced by imposing additional constraints in the designed framework. The proposed design technique is illustrated by considering several numerical examples that show the superiority of the proposed technique over the existing methods.

Integral Control of Stable Negative-Imaginary Systems Preceded by Hysteresis Nonlinearity

IEEE Transactions on Automatic Control

In this note, constant reference tracking using integral control for negative-imaginary (NI) syst... more In this note, constant reference tracking using integral control for negative-imaginary (NI) systems preceded by hysteresis nonlinearity is addressed. The hysteresis nonlinearity is considered to be slope-restricted, though no specific modeling framework is exploited. It is effectively shown that integral tracking controllers are guaranteed to exist when a stable NI system with sign-definite dc-gain is preceded by such hysteresis nonlinearities. When the dc-gain is negative-definite, under positive feedback configuration with positive slope-restricted hysteresis, it is established that the integral controller gain can be any positive diagonal matrix. The development of the proposed model-independent inversion-free scheme is carried out in general state-space setting and is applicable for multiple-input multiple-output systems with decoupled hysteresis nonlinearities. Effectiveness of the results is illustrated with examples.

On decentralized integral controllability of stable negative-imaginary systems and some related extensions

Automatica

Abstract This paper exploits the decentralized integral controllability (DIC) of stable negative-... more Abstract This paper exploits the decentralized integral controllability (DIC) of stable negative-imaginary (NI) systems with non-singular DC-gain matrix to develop a constant input tracking framework with failure tolerance property in the event of sensor and/or actuator faults. By virtue of the DIC property of NI systems, it is shown that a positive feedback interconnection of two NI systems, of which one is a decentralized integrator system with non-negative gains and the other one is a stable NI system having negative definite DC-gain matrix, is internally stable. This is in contrast to the existing results where, for internal stability, at least one of the systems needs to be strictly negative-imaginary (SNI). Further it is shown that, in a positive feedback interconnection, stable NI systems with negative definite DC-gain matrix exhibit integral controllability (IC) property for any positive value of the integral gain k , which is a distinct property of stable NI systems having negative definite DC-gain matrix since the existing notion of IC for LTI systems offers only a finite range of k . Using the DIC property and the eigenvalue loci technique, some new results and research directions for the NI systems have also been presented in this paper.

Stability analysis and controller design for Lur'e system with hysteresis nonlinearities: a negative-imaginary theory based approach

International Journal of Control

ABSTRACT In this paper, absolute stability condition is investigated when a hysteresis nonlineari... more ABSTRACT In this paper, absolute stability condition is investigated when a hysteresis nonlinearity is connected to a linear subsystem via positive feedback in Lur'e system framework. In particular, the nonlinearity is considered to belong to the time-invariant slope-restricted counter-clockwise hysteresis class. An absolute stability criterion is proposed in terms of the negative-imaginary system properties. In effect, the stability condition requires the linear subsystem to belong to the strongly strict negative-imaginary (SSNI) system class along with satisfying a matrix condition involving the DC-gain of the linear subsystem and the slope-upper-bounds of the nonlinearities. Compliance to the conditions guarantees asymptotic convergence of state-trajectories to an equilibrium set. Invoking the stability result and exploiting the relaxed minimality assumption of SSNI systems, a static state-feedback synthesis method is proposed to ensure absolute stability for such hysteretic systems. Tractable conditions in the form of linear matrix inequalities can be solved to obtain a stabilising state-feedback gain matrix. Finally, a numerical example of multi-input–multi-output system is presented to illustrate the usefulness of the proposed results.

Design of H[sub ∞] Loop-Shaping Controller for LTI System With Input Saturation: Polytopic Gain Scheduled Approach

Journal of Dynamic Systems, Measurement, and Control

This paper demonstrates the design of H∞ loop-shaping controller for a linear time invariant (LTI... more This paper demonstrates the design of H∞ loop-shaping controller for a linear time invariant (LTI) system with input saturation constraint. The design problem has been formulated in the four-block H∞ synthesis framework, which is equivalent to normalized coprime factor robust stabilization problem. The shaped plant is represented as a polytopic linear parameter varying (LPV) system while saturation nonlinearity is considered. For a polytopic model, the LTI H∞ loop-shaping controllers have been designed at each vertex of the polytope using linear matrix inequalities, and subsequently controllers are scheduled by adopting a certain interpolation procedure. The proposed controller ensures the stability and robust L2-performance of the closed-loop system due to vertex property of the polytopic LPV shaped plant. The effectiveness of the design method has been illustrated through a numerical example.

On LTI output strictly negative-imaginary systems

Systems & Control Letters

Abstract This paper deals with the notion of output strictly negative-imaginary systems. A defini... more Abstract This paper deals with the notion of output strictly negative-imaginary systems. A definition is given for the class of output strictly negative-imaginary systems and a lemma is proposed to test the necessary and sufficient conditions required to satisfy output strictly negative-imaginary system properties. A set theoretic relationship is established between the existing class of strictly negative-imaginary systems and the newly defined output strictly negative-imaginary systems class. A stability analysis result for interconnected systems with positive feedback is presented while one of the systems is negative-imaginary and the other one is output strictly negative-imaginary, contrary to the existing results where at least one of the systems in the interconnection belongs to the strictly negative-imaginary class. Several numerical examples have been studied to demonstrate the proposed results.

An observer-based control scheme using negative-imaginary theory

Automatica

This paper presents a full-order state observer-based scheme that transforms a causal, LTI, minim... more This paper presents a full-order state observer-based scheme that transforms a causal, LTI, minimally realized system into a strongly strict negative-imaginary system by defining an auxiliary output based on the observed states. The auxiliary output is used for closed-loop control with positive feedback invoking the internal stability condition of negative-imaginary theory. A set of LMI conditions is derived that determines the value of a design parameter required for the proposed scheme to transform a given system with a minimal state-space realization into a strongly strict negative-imaginary system. The proposed scheme is applicable for both stable/unstable and square/non-square systems. In this paper, the framework is further explored for robustness analysis of uncertain systems and numerical examples are given to elucidate effectiveness of the proposed results.

New control allocation algorithms in fixed point framework for overactuated systems with actuator saturation

International Journal of Control, 2016

ABSTRACTIn this paper, two control allocation algorithms have been proposed for overactuated syst... more ABSTRACTIn this paper, two control allocation algorithms have been proposed for overactuated systems. The algorithms are developed by formulating constrained control allocation problem into an equivalent fixed point framework. The first algorithm follows sequential solving method while the other one involves a zero finding technique by the Newton method. In order to consider limiting constraints, the saturation function has been taken into account that leads to a nonsmooth zero finding problem and the proposed method guarantees superlinear convergence. The second algorithm is easy to implement and faster than the algorithm developed based on the sequential solving technique. To demonstrate the effectiveness of the proposed algorithms, a detail simulation study has been carried out, in which one example considers both the actuator rate and amplitude constraints.

A cosed-loop data based test for robust performance improvement in iterative identification and control redesigns

Automatica a Journal of Ifac the International Federation of Automatic Control, 2012

Design of static Hºº loop shaping controller in four-block framework using LMI approach

Automatica a Journal of Ifac the International Federation of Automatic Control, 2008

Design of Robust Load Frequency Controller: H8 Loop Shaping Approach

Electr Power Compon Syst, 2007

Tweaking Metabolic Networks: A Design Method

INAE Letters, 2016

A robust synthesis technique is devised for synergism and saturation systems, commonly known as S... more A robust synthesis technique is devised for synergism and saturation systems, commonly known as S-systems, for steering steady-states of the anaerobic fermentation pathway (AFP) of Saccharomyces cerevisae. The stability, steady-state error and robustness aspects are analyzed. The synthesis problem is framed in a computationally efficient convex optimization framework. The linear matrix inequalities are formulated for minimization of steady-state error, improvement of robustness and utilization of minimum control inputs ensuring the stability of the synthetic AFP.

format_quoteMinimization of perturbation sensitivity enhances robustness in the synthetic metabolic model, allowing better control of metabolic pathways.format_quote

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A Control Theoretic Approach for Solving Underdetermined Problems and Its Application to Control Allocation

Journal of Dynamic Systems, Measurement, and Control, 2016

In this paper, a new iterative algorithm is developed using control theoretic approach to find th... more In this paper, a new iterative algorithm is developed using control theoretic approach to find the minimum norm solution of underdetermined problems. The minimum norm solution is obtained by applying the H∞ optimization technique. The accuracy and convergence rate of the proposed algorithm are ensured using the framework of linear feedback control theory. The performances of the proposed method, the QR decomposition method, and the least square minimal residue (LSMR) method are compared numerically. The number of iterations in the proposed algorithm is comparable with the LSMR method. Finally, the developed algorithm is applied to the control allocation problem and its effectiveness is demonstrated through a detailed simulation study.

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