Conservative Stability Criteria Research Articles

Robust stability criteria for uncertain linear systems with interval time-varying delay

This paper considers 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. Less conservatism of the proposed stability criteria is attributed to the delay-central point method of stability analysis, wherein the delay interval is partitioned into two subintervals of equal length, and the time derivative of a candidate Lyapunov-Krasovskii functional based on delay decomposition technique is evaluated in each of these delay segments. 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-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional; instead, they are dealt using tighter integral inequalities. The proposed analysis subsequently yields a stability condition in convex LMI framework that can be solved using standard numerical packages. For deriving robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties, are considered. The effectiveness of the proposed stability criteria is validated through standard numerical examples.

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In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

Passive fuzzy controller design for stochastic Takagi—Sugeno fuzzy systems with time-varying delay

This paper discusses the issue of stability and stabilization for the non-linear stochastic systems with time-varying delay subject to passivity performance. Based on the fuzzy modelling approach, the non-linear systems can be represented by a stochastic T—S fuzzy model whose consequent part is described by linear differential equations with a multiplicative noise term. For analysing the stability of the stochastic T—S fuzzy model, the less conservative stability criterion derived by Itô's formula and the Lyapunov—Krasovskii function is proposed as a linear matrix inequality (LMI) problem. Furthermore, the passivity theory is employed to discuss the external disturbance effect on the considered system. Through applying the above techniques, the sufficiency conditions are derived to design fuzzy controllers such that the stochastic T—S fuzzy model with time delay is asymptotically stable and passive in the mean square. Finally, two numerical examples are proposed to show the application and effectiveness of the proposed fuzzy controller design method.

Delay-range-dependent stability criterion for interval time-delay systems with nonlinear perturbations

In this paper, we consider the problem of robust stability for a class of linear systems with interval time-varying delay under nonlinear perturbations using Lyapunov-Krasovskii (LK) functional approach. By partitioning the delay-interval into two segments of equal length, and evaluating the time-derivative of a candidate LK functional in each segment of the delay-interval, a less conservative delay-dependent stability criterion is developed to compute the maximum allowable bound for the delay-range within which the system under consideration remains asymptotically stable. In addition to the delay-bi-segmentation analysis procedure, the reduction in conservatism of the proposed delay-dependent stability criterion over recently reported results is also attributed to the fact that the time-derivative of the LK functional is bounded tightly using a newly proposed bounding condition without neglecting any useful terms in the delay-dependent stability analysis. The analysis, subsequently, yields a stable condition in convex linear matrix inequality (LMI) framework that can be solved non-conservatively at boundary conditions using standard numerical packages. Furthermore, as the number of decision variables involved in the proposed stability criterion is less, the criterion is computationally more effective. The effectiveness of the proposed stability criterion is validated through some standard numerical examples.

Stabilization analysis and implementation for MIMO NCS with time‐varying delays

AbstractThis paper is concerned with the design of output feedback controllers for a class of maximum input maximum output networked control systems (NCSs). In view of NCSs with many independent sensors and actuators, a discrete‐time model with multiple time‐varying delays is proposed. By constructing a novel Lyapunov–Krasovskii functional, a new less conservative stability criterion is developed in terms of linear matrix inequality. On the basis of the obtained stability condition, a static output feedback controller can be designed by applying an iterative algorithm. Both simulation and practical experiment results are given to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

Stability and H∞ Performance Analysis for Markovian Jump Systems with Time-varying Delay and Partial Information on Transition Probabilities⋆

AbstractThis paper focuses on stability and H∞ performance analysis for a class of continuous-time Markovian jump systems with unknown transition probability and time-varying delay. Based on the free-connection weighting matrix method, the less conservative stability criterion and bounded real lemma (BRL) of Markovian jump systems with time-varying delay are obtained by considering the influence of partly unknown transition probability or completely unknown transition probability. Finally, numerical examples are given to illustrate the effectiveness and the merits of the proposed method.

Stability of genetic regulatory networks with interval time‐varying delays and stochastic perturbation

AbstractThis paper studies the delay‐dependent stability for genetic regulatory networks with both interval time‐varying delays and stochastic perturbation. By considering the relationship among the time‐varying delays, its upper bound and their difference, and introducing an improved‐free‐weighting matrix (IFWM) approach, some less conservative stability criteria are proposed without ignoring any useful terms in the weak infinitesimal operator of the Lyapunov‐Krasovskii functional. Two numerical examples are given to illustrate the effectiveness and the reduced conservativeness of the obtained results.© 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices

This paper focuses on stability and stabilization for a class of continuous-time Markovian jump systems with partial information on transition probability. The free-connection weighting matrix method is proposed to obtain a less conservative stability criterion of Markovian jump systems with partly unknown transition probability or completely unknown transition probability. As a result, a sufficient condition for the state feedback controller design is derived in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness and the merits of the proposed method.

Stability analysis for T–S fuzzy systems with interval time‐varying delays and nonlinear perturbations

AbstractThis paper is concerned with the problem of the robust stability for T–S fuzzy systems with interval time‐varying delay and nonlinear perturbations. The key features of the approach include the introduction of uncorrelated augmented matrix items into the Lyapunov functional and the use of some appropriate integral inequalities. Unlike the existing methodologies, the proposed approach involves neither free weighting matrices nor any model transformation. It can, however, lead to much less conservative stability criteria than the existing ones for the systems under consideration. The cases of perturbations are assumed to both nonlinear time‐varying perturbations and time‐varying uncertainties in linear fractional form. Numerical examples show that the obtained results are less conservative than the existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd.

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.

New stability criteria for continuous-time systems with interval time-varying delay

The authors investigate the stability for continuous-time systems with interval time-varying delay. To deal with the non-linear time-varying coefficients derived from Jensen's integral inequality, a well-known feature of the sum of these coefficients is utilised. Combining with a delay partition method, the upper bound of the derivative of the Lyapunov functional can be estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. New less conservative stability criteria are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed results.

A novel delay-dependent criterion for delayed neural networks of neutral type

This Letter considers a robust stability analysis method for delayed neural networks of neutral type. By constructing a new Lyapunov functional, a novel delay-dependent criterion for the stability is derived in terms of LMIs (linear matrix inequalities). A less conservative stability criterion is derived by using nonlinear properties of the activation function of the neural networks. Two numerical examples are illustrated to show the effectiveness of the proposed method.

Less conservative delay-dependent stability criteria for neural networks with time-varying delays

This paper is concerned with the stability for static neural networks with time-varying delays. With an appropriate Lyapunov functional formulated, a new technique is proposed to up bound the derivative of the Lyapunov functional. A delay-dependent stability criterion is obtained by proving the bound negative definite with convex combination methods. The delay-dependent stability criterion is simpler and less conservative than some existing ones. Both delay-independent and delay-dependent criteria are obtained, which can be checked easily using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed results.

Delay-dependent Stability for Systems with Fast-varying Neutral-type Delays via a PTVD Compensation

Abstract The stability for a class of linear neutral systems with time-varying delays is studied in this paper, where delay in neutral-type term includes a fast-varying case (i.e., the derivative of delay is more than one), which has never been considered in current literature. The less conservative delay-dependent stability criteria for this system are proposed by applying new Lyapunov-Krasovskii functional and novel polynomials with time-varying delay (PTVD) compensation technique. The aim to deal with systems with fast-varying neutral-type delay can be achieved by using the new functional. The benefit brought by applying the PTVD compensation technique is that some useful elements can be included in criteria, which are generally ignored when estimating the upper bound of derivative of Lyapunov-Krasovskii functional. A numerical example is provided to verify the effectiveness of the proposed results.

Improved delay-dependent absolute stability of Lur’e systems with time-delay

The problem of absolute stability of Lur’e systems with time-delay is investigated in this paper. By employing a new Lyapunov-Krasovskii functional with the idea of N-segmentation of delay length, less conservative delay-dependent stability criteria are obtained and formulated in the form of linear matrix inequalities (LMIs). Numerical example shows that the results obtained in this paper are better than existing ones.

New delay-dependent stability results for discrete-time recurrent neural networks with time-varying delay

This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By using the discrete Jensen inequality and the sector bound conditions, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Robust stability analysis of uncertain systems with two additive time-varying delay components

This paper is concerned with stability analysis for uncertain systems. The systems are based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components and parameter uncertainties. Numerical examples show that the proposed criteria are effective and are an improvement over some existing results in the literature.

New stability criteria for discrete-time recurrent neural networks with time-varying delay

Abstract This paper studies the problem of stability analysis for discrete-time recurrent neural networks (DRNNs) with time-varying delays. By defining a more general type of Lyapunov functionals and combining the discrete Jensen inequality, a new less conservative delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs) under a weak assumption on the activation functions. By using a delay decomposition method, a further improved stability criterion is also derived. It is shown that the newly obtained results are less conservative than the existing ones. Meanwhile, the computational complexity of the newly obtained stability conditions is reduced since less variables are involved. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Improved delay-dependent absolute stability and robust stability for a class of nonlinear systems with a time-varying delay

This paper investigates the problem of the absolute stability of Lur'e systems with a time-varying delay. By considering the relationships among the time-varying delay, its upper bound, and the difference between them, less conservative delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities, without ignoring any useful terms in the derivative of a Lyapunov–Krasovskii functional. Numerical example shows that the results obtained in this paper are better than the previous results. Copyright © 2009 John Wiley & Sons, Ltd.

New robust exponential stability analysis for uncertain neural networks with time-varying delay

In this paper, the global robust exponential stability is considered for a class of neural networks with parametric uncertainties and time-varying delay. By using Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the derivative of the Lyapunov functional, some less conservative exponential stability criteria are derived in terms of linear matrix inequalities (LMIs). Numerical examples are presented to show the effectiveness of the proposed method.