Simple stability conditions of linear discrete time systems with multiple delay

In this paper we have established a new Lyapunov-Krasovskii method for linear discrete time systems with multiple time delay. Based on this method, two sufficient conditions for delay-independent asymptotic stability of the linear discrete time systems with multiple delays are derived in the shape of Lyapunov inequality. Numerical examples are presented to demonstrate the applicability of the present approach

On delay-dependent robust stability under model transformation of some neutral systems

summary:This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability are given in terms of the existence of positive definite solutions of LMIs

Quasi-Linear Differential-Deference Game of Approach

This is a post-peer-review, pre-copyedit version of a book chapter that is part of “V. A. Sadovnichiy, M. Z. Zgurovsky (eds.). Modern Mathematics and Mechanics. Understanding Complex Systems”. The final authenticated version is available online at: https://link.springer.com/chapter/10.1007/978-3-319-96755-4_26The paper is devoted to the games of approach. We consider a controlled object whose dynamics is described by the linear differential system with a pure time delay or the differential-difference system with commutative matrices in Euclidean space. The approaches to the solutions of these problems are proposed which based on the Method of Resolving Functions and the First Direct Method of L.S. Pontryagin. The guaranteed times of the game termination are found, and corresponding control laws are constructed. The results are illustrated by a model example

Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay

This paper is concerned with the problems of stability analysis and stabilization for discrete-time Takagi-Sugeno fuzzy systems with time-varying state delay. By constructing a new fuzzy Lyapunov function and by making use of novel techniques, an improved delay-dependent stability condition is obtained, which is dependent on the lower and upper delay bounds. The merit of the proposed stability condition lies in its reduced conservatism, which is achieved by avoiding the utilization of some bounding inequalities for the cross products between two vectors. Then, delay-dependent stabilization approach based on a parallel distributed compensation scheme is developed for both state feedback and observer-based output feedback cases. The proposed stability and stabilization conditions are formulated in terms of linear matrix inequalities, which can be solved efficiently by using existing optimization techniques. Two illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper. © 2008 IEEE.published_or_final_versio

Sliding mode control of systems with time-varying delays via descriptor approach

International audienceIn this paper, we combine a descriptor approach to stability and control of linear systems with time-varying delays, which is based on the Lyapunov-Krasovskii techniques, with a recent result on sliding mode control of such systems. The systems under consideration have norm-bounded uncertainties and uncertain bounded delays. The solution is given in terms of linear matrix inequalities (LMIs) and improves the previous results based on other Lyapunov techniques. A numerical example illustrates the advantages of the new method