Robust stability analysis for time-delay systems using the integral quadratic constraint approach

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

The method of Implicit Lyapunov-Krasovski Functional (ILKF) for stability analysis of time-delay systems is introduced. Theorems on Lyapunov, asymptotic, (hyper) exponential, finite-time and fixed-time stability analysis using ILKF are presented. The hyper exponential stabilization algorithm for a time-delay system is presented. The theoretical result is supported by numerical simulation.

ABSTRACTThis paper investigates the problem of exponential stability analysis of linear time-delay systems. First, based on the Gram-Schmidt-based integral inequality and the Taylor expansion of exponential function, we develop a new weighted multiple integral inequality called Taylor expansion-based weighted integral inequality. Second, a new Lyapunov-krasovskii functional is constructed, and then, with the help of the Taylor expansion-based inequality, a new exponential stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are presented to show the effectiveness of the newly established stability criterion.

This paper studies stability analysis of linear time-invariant time-delay feedback systems consisting of a finite-dimensional system and a pure delay. The continuous-time state transition is described by the monodromy operator in discrete-time through the lifting technique, and a stability condition in terms of its spectral radius is first restated in terms of the norm of a power of the operator. Quasi-finite-rank approximation is then applied on the power of the operator, and by evaluating the effect of the approximation error on the norm, a new necessary and sufficient stability condition is given finally.

Robust stability analysis problem is considered for linear time-invariant systems subject to perturbations of parameters that vary smoothly in time. The problem is formulated by describing the uncertainty in the form of a region-of-variation that covers all possible trajectories obtained by plotting the variation of the parameter at a certain time versus the parameter itself at that same instant of time. In this fashion, the possible and very probable correlation between the parameter and its variation is taken into account. The problem is elaborated on via an integral quadratic constraints approach and, based on a main result relying on the swapping lemma, robust stability analysis tests are derived for polytopic regions of variation as well as for regions with generic descriptions expressed in terms of matrix inequalities. The tests for polytopic regions-of-variation are based on the convex hull and Pólya relaxation approaches, whereas the test for general regions relies on the sum-of-squares relaxation approach. The new tests offer significant reduction in conservatism at the cost of extra computational complexity.

Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

ABSTRACTThis paper addresses the problem of robust stabilisation of nD hybrid systems described by Roesser model. The model is in a descriptor form where all the system matrices are corrupted by uncertainty in a general form as implicit linear fractional representations . Based on the S-procedure technique, robust stability and robust stabilisation conditions are established for hybrid systems. Simulation example is provided in order to illustrate the relevance of our approach.

This paper addresses the problem of the stability analysis for a linear time-delay systems via a robust analysis approach and especially the quadratic separation framework. To this end, we use the Bessel inequality for building operators that depend on the delay. They not only allow us to model the system as an uncertain feedback system but also to control the accuracy of the approximations made. Then, a set of LMIs conditions are proposed which tends on examples to the analytical bounds for both delay dependent stability and delay range stability.

The robust stability of linear continuous-time uncertain systems in polytopic domains is investigated in this paper. The uncertain parameters are assumed as time-varying with bounded rates of variation. The robust stability conditions are obtained from the definition of a Lyapunov function with a particular structure, depending on integer powers κ of the dynamic uncertain matrix of the system. As a consequence, parametrized linear matrix inequalities conditions are obtained in terms of κ. As κ grows, the robust stability conditions can take into account bounds on the successive time-derivatives of the uncertain parameters, reducing the conservativeness of the evaluations. Numerical examples illustrate the effectiveness of the proposed methodology.

In this article, the issue of robust stability analysis for a sort of uncertain neutral system with mixed time-varying delays is studied. A new Lyapunov–Krasovskii functional comprising quadruple-integral term is introduced so as to develop a less conservative stability condition. A novel discrete and neutral delay-dependent stability criterion based on linear matrix inequalities is given using delay-central point method as well as reciprocally convex combination approach, which is derived by integral inequality approach. Compared with the existing literature, this criterion can greatly reduce the complexity of theoretical derivation and computation. Finally, three numerical comparative examples are designated to verify the superiority of the proposed approach in reducing the conservation of conclusion.

Robust stability analysis of Markov jump standard genetic regulatory networks with mixed time delays and uncertainties

This paper discusses the problem of robust delay-dependent exponential stability for a class of uncertain stochastic systems with time-varying delay. The uncertainty is assumed to be of norm-bounded form. A less conservative robust exponential stability condition is derived by using a new Lyapunov–Krasovskii functional and a free-weighting matrix method in terms of linear matrix inequalities. Two numerical examples are given to illustrate the effectiveness of the proposed method.

A new quasi-finite-rank approximation of compression operators on [formula omitted] with applications to sampled-data and time-delay systems: Piecewise linear kernel approximation approach

Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays