K. Ramakrishnan

Improved delay-range-dependent robust stability criteria for a class of Lur’e systems with sector-bounded nonlinearity

Abstract In this paper, the problem of delay-dependent stability of a class of uncertain Lur’e systems of neutral type with interval time-varying state delay and sector-bounded nonlinearity has been considered based on Lyapunov–Krasovskii functional approach. By constructing a candidate Lyapunov–Krasovskii (LK) functional, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs). The reduction in conservatism of the proposed stability criteria over recently reported results is attributed to the candidate LK functional used in the delay-dependent stability analysis, and to the tighter bounding of the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability condition in convex LMI framework, and is solved non-conservatively at boundary conditions using standard numerical packages. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay

In this paper, we consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

Delay-dependent robust stability criteria for linear uncertain systems with interval time varying delay

This paper investigates the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay, and proposes less conservative stability criteria for computing the maximum allowable bound of the delay range. The proposed stability criteria are based on the delay central point technique wherein the delay interval is partitioned into two sub-intervals of equal length, and the time variation of a Lyapunov-Krasovskii functional is considered individually for each of these segments in order to reduce the conservatism of the stability criteria. For robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties are considered. In deriving the stability conditions in LMI framework, neither model transformations, nor bounding techniques using free-weighting matrix variables are employed for dealing the cross-product terms; instead, they are dealt using tighter integral inequalities. This, in turn, makes the proposed approach computationally more efficient and simple. Subsequently, the results obtained are less conservative in the range of allowable delay bound. The effectiveness of the proposed stability criteria is validated through numerical examples.

Robust stability criterion for Markovian jump systems with nonlinear perturbations and mode-dependent time delays

In this paper, the problem of delay-dependent stability of a class of uncertain Markovian jump systems with mode-dependent interval time-varying delay and nonlinear perturbations is considered using Lyapunov–Krasovskii (LK) functional approach. In the proposed stability analysis, by exploiting a candidate LK functional and by imposing tighter bounding on the cross-terms using minimal number of slack matrix variables, a less conservative delay-dependent stability criterion is presented in linear matrix inequality framework. The effectiveness of the proposed stability criterion over some of the recently reported results is demonstrated through standard numerical examples.

Delay-dependent stability criteria for linear systems with multiple time-varying delays

This paper is concerned with the delay-dependent stability analysis of a class of linear system with multiple time-varying delays. By using appropriate Lyapunov-Krasovskii functional and integral inequality lemmas, a simple delay-dependent stability criterion is proposed in LMI framework to estimate the maximum allowable bound/range of the time-delay within which the system under consideration remains asymptotically stable. The simplicity of the criterion stems from the fact that neither any terms are ignored in the analysis while dealing with the cross product terms, nor any free-weighting matrices are introduced in the theoretical derivation to counter them. Hence the resulting LMI (stability criterion) has no additional matrix variables apart from those used in the Lyapunov-Krasovskii functional. This, in turn, makes the proposed approach less conservative as well as computationally attractive. To validate the effectiveness of the proposed stability criterion, the systems considered are i) a networked control system with dynamic output and static state feedback, and ii) a multiple delay system with two time-varying delays.

Delay-dependent stability analysis of linear system with additive time-varying delays

In this paper, a new delay-dependent stability criterion is presented for a class of linear system with additive time varying delay elements in the state vector. By using an appropriate Lyapunov-Krasovskii functional and integral inequality lemmas, a simple delay-dependent stability criterion is proposed in LMI framework that estimates the maximum allowable bound of the time delays within which the system under consideration remains asymptotically stable. The simplicity of the criterion stems from the fact that neither any terms are ignored in the analysis while dealing with the cross product terms, nor any free-weighting matrices are introduced in the theoretical derivation to counter them. The proposed criterion is computationally attractive, and it provides less conservative results than the existing results. A numerical example with two additive delay elements is considered to test the effectiveness of the proposed method.

Reciprocal convex approach to delay-dependent stability of uncertain discrete-time systems with time-varying delay

In this paper, we consider the problem of delay-dependent stability of a class of uncertain linear discrete-time systems with time-varying delay using Lyapunov functional approach. By exploiting a candidate Lyapunov functional, and using reciprocal convex approach in the delay-dependent stability analysis, a less conservative robust stability criterion is derived in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed criterion over a recently reported result is validated using a standard numerical example.

Improved Stability Criteria for Lurie Type Systems with Time-varying Delay

Abstract In this technical note, we present a new stability analysis procedure for ascertaining the delay-dependent stability of a class of Lurie systems with time-varying delay and sector-bounded nonlinearity using Lyapunov-Krasovskii (LK) functional approach. The proposed analysis, owing to the candidate LK functional and tighter bounding of its time-derivative, yields less conservative absolute and robust stability criteria for nominal and uncertain systems respectively. The effectiveness of the proposed criteria over some of the recently reported results is demonstrated using a numerical example.

An improved delay-dependent stability criterion for neutral systems with mixed time-delays and nonlinear perturbations

In this paper, we consider the problem of delay-dependent robust stability of a class of linear neutral systems with mixed time-delays and nonlinear perturbations using Lyapunov-Krasovskii functional approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, a less conservative robust delay-dependent stability criterion is proposed in terms of matrix inequalities. Reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the candidate LK functional, and to tighter bounding of the time-derivative of the functional without neglecting any useful terms in the delay-dependent stability analysis. The analysis, eventually, culminates into a stability condition in convex LMI framework, and is solved non-conservatively at boundary conditions. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.