Robust exponential stability for uncertain time-varying delay systems with delay dependence

This paper investigates the exponential stability problem for uncertain time-varying delay systems. Based on the Lyapunov-Krasovskii functional method, delay-dependent stability criteria have been derived in terms of a matrix inequality (LMI) which can be easily solved using efficient convex optimization algorithms. These results are shown to be less conservative than those reported in the literature. Four numerical examples are proposed to illustrate the effectiveness of our results.     

New approaches to stability analysis for time-varying delay systems

In this paper, two new estimation approaches namely delay-dependent-matrix-based (DDMB) reciprocally convex inequality approach and DDMB estimation approach, are introduced for stability analysis of time-varying delay systems. Different from existing estimation techniques with constant matrices, the estimation approaches are with delay-dependent matrices, which can employ more free matrices and utilize more information of both time delay and its derivative. Based on the estimation approaches, less conservative stability criteria with lower computational complexity are derived in the form of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the advantages of the proposed methods.     

New criterion for finite-time stability of linear discrete-time systems with time-varying delay

This paper is concerned with the problem of finite-time stability analysis of linear discrete-time systems with time-varying delay. The time-varying delay has lower and upper bounds. By choosing a novel Lyapunov–Krasovskii-like functional, a new sufficient condition is derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold during a fixed time interval. Then, the corresponding corollary is developed for the case of constant time delay. Numerical examples are provided to demonstrate the effectiveness and merits of the proposed method.     

Relaxed stability criteria of time-varying delay systems via delay-derivative-dependent slack matrices

This paper is focused on delay-dependent stability problem of time-varying delay systems. By introducing delay-derivative-dependent slack matrices, relaxed stability conditions are derived based on Lyapunov-Krasovskii functional approach. As the delay-derivative-dependent slack matrices provide extra freedom to optimize the Lyapunov matrices, less conservative results are obtained. Two benchmark examples are provided to verify the effectiveness of the proposed approach.     

Robust finite-time stability of singular nonlinear systems with interval time-varying delay

The problem of robust finite-time stability (RFTS) for singular nonlinear systems with interval time-varying delay is studied in this paper. Some delay-dependent sufficient conditions of RFTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii functional (LKF) method and singular analysis technique. Two examples are provided to show the applications of the proposed criteria.     

Switching signal design for exponential stability of discrete switched systems with interval time-varying delay

The switching signal design for global exponential stability of discrete switched systems with interval time-varying delay is considered in this paper. Some LMI conditions are proposed to design the switching signal and guarantee the global exponential stability of switched time-delay system. Some nonnegative inequalities are used to reduce the conservativeness of the systems. Finally, two numerical examples are illustrated to show the main result.     

A necessary and sufficient condition for delay-independent stability of linear time-varying neutral delay systems

In this paper, stability analysis of linear time-varying neutral delay systems is considered. A necessary and sufficient condition for delay-independent global asymptotic stability of such systems is derived. Eventually, two examples are given in order to show the results established.     

Improved stability conditions of time-varying delay systems based on new Lyapunov functionals

This paper is concerned with the stability analysis of time-varying delay systems. Unlike the construction of augmented Lyapunov functional and multiple integral Lyapunov functional, novel three Lyapunov functionals are suggested which are delay product type functions and lead to less conservative results. Based on newly developed Lyapunov functionals, three stability criteria are derived and their superiority is described by three numerical examples.     

A generalized multiple-integral inequality and its application on stability analysis for time-varying delay systems

This paper is concerned with the stability analysis of time-delay systems. Lyapunov–Krasovskii functional method is utilized to obtain stability criteria in the form of linear matrix inequalities. The main purpose is to obtain less conservative stability criteria by reducing the estimation gap of the time derivative of the constructed Lyapunov–Krasovskii functional. First, a generalized multiple-integral inequality is put forward based on Schur complement lemma. Then, some special cases of the proposed generalized multiple-integral inequality are given to estimate single and double integral terms in the derivative of Lyapunov–Krasovskii functional. Furthermore, less conservative stability criteria are derived. Finally, three examples are given to illustrate the improvement of the proposed criteria.     

New stability and stabilization criteria for a class of fuzzy singular systems with time-varying delay

This paper deals with the stability analysis and fuzzy stabilizing controller design for fuzzy singular systems with time-varying delay. The time-varying delay is composed of two parts: constant part and time-varying part. Based on the idea of delay partitioning, a new Lyapunov–Krasovskii functional is proposed to develop the new delay-dependent stability criteria, which ensures the considered system to be regular, impulse-free and stable. Furthermore, the desired fuzzy controller gains are also presented by solving a set of strict linear matrix inequalities (LMIs). Some numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.     

Robust stability criteria for uncertain systems with interval time-varying delay based on multi-integral functional approach

This paper is concerned with the robust stability analysis for uncertain systems with interval time-varying delay. In order to make full use of the delay information, a novel Lyapunov–Krasovskii functional (LKF) containing single, double, triple and quadruple integral terms is introduced, and a triple-integral state variable is also used. Then, by using the Wirtinger-based single and double integral inequality, introducing some positive scalars, the derivative of the constructed LKF is estimated more accurately. As a result, some stability criteria are derived, which have less conservatism and decision variables. Numerical examples are also given to show the effectiveness of the proposed method.     

Mean-square exponential stability for a class of discrete-time nonlinear singular Markovian jump systems with time-varying delay

This paper investigates the problem of mean-square exponential stability for a class of discrete-time nonlinear singular Markovian jump systems with time-varying delay. The considered systems are with mode-dependent singular matrices _Er(k)$E_{r\left(k\right)}$. By using the free-weighting matrix method and the Lyapunov functional method, delay-dependent sufficient conditions which guarantee the considered systems to be mean-square exponentially stable are presented. Finally, some numerical examples are employed to demonstrate the effectiveness of the proposed methods.     

Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations

The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature.     

Further results on delay-dependent stability criteria of discrete systems with an interval time-varying delay

This paper deals with stability of discrete-time systems with an interval-like time-varying delay. By constructing a novel augmented Lyapunov functional and using an improved finite-sum inequality to deal with some sum-terms appearing in the forward difference of the Lyapunov functional, a less conservative stability criterion is obtained for the system under study if compared with some existing methods. Moreover, as a special case, the stability of discrete-time systems with a constant time delay is also investigated. Three numerical examples show that the derived stability criteria are less conservative and require relatively small number of decision variables.     

Stability analysis for interval time-varying delay systems based on time-varying bound integral method

This paper addresses the new stability analysis method for systems with interval time-varying delay. By taking single-integral and double-integral terms with time-varying bound into consideration, a new Lyapunov–Krasovskii functional is defined. Then reciprocally convex approach and some transformations are used to estimate the derivative of the constructed functional less conservatively, and as a result, some new stability criteria are obtained in terms of the quadratic convex combination, which are less conservative and have less decision variables. Two well-known examples are also given to illustrate the advantage of the main results.     

State bounding for nonlinear time-varying systems with delay and disturbance

This paper deals with the problem of state bounding for a class of nonlinear time-varying systems with delay and bounded disturbance. By using a model transformation and an approach developed in positive systems, new delay-dependent explicit conditions have been established to guarantee all the state trajectories of the system converge exponentially within a ball. Two illustrative examples are given to show that the obtained results can be applied to some cases not covered by preceding results.     

Advanced stability criteria for linear systems with time-varying delays

This paper investigates a stability problem for linear systems with time-varying delays. By constructing suitable augmented Lyapunov–Krasovskii functionals, improved stability criteria under various conditions of time-varying delays are derived within the framework of linear matrix inequalities (LMIs). Moreover, to reduce the computational burden caused by the non-convex term including h²(t), how to deal with it is applied by estimating it to the convex term including h(t). Finally, three illustrative examples are given to show the effectiveness of the proposed criteria.     

Improved stability criteria for linear systems with time-varying delays

This paper is concerned with the stability analysis of linear systems with time-varying delays. First, by introducing the quadratic terms of time-varying delays and some integral vectors, a more suitable Lyapunov-Krasovskii functional (LKF) is constructed. Second, two new delay-dependent estimation methods are developed in the stability analysis of linear system with time-varying delays, which include a reciprocally convex matrix inequality and an integral inequality. More information about time-varying delays and more free matrices are introduced into the two estimation approaches, which play a key role for obtaining an accurate upper bound of the integral terms in time derivative of LKFs. Third, based on the novel LKFs and new estimation approaches, some less conservative criteria are derived in the form of linear matrix inequality (LMI). Finally, three numerical examples are applied to verify the advantages and effectiveness of the newly proposed methods.