An investigation of the input-to-state practical stability (ISpS) and integral (iISpS) nonlinear systems with time delays (NSWTDs) is presented in this paper. The ISpS iISpS are obtained by using a continuously differentiable Lyapunov–Krasovskii functional (LKF) within-definite derivative, which generalizes classical LKF positive definite derivative. As result, uniform asymptotic (UPAS) criteri...

In this paper, we study the stability of a wide class of switched systems using stability preserving mappings. By considering an existing result and extending it to a general class of switched systems, we show that stability preserving mappings constitute an important and practical tool in stability analysis and design of switched systems.

Abstract: This paper deals with stability of discrete-time nonlinear Lur’e-type systems. Through the singular perturbations technique, the original system is reduced to a block-diagonal form with slow and fast decoupled modes. Stability conditions of the two-time-scale decoupled model based on Borne-Gentina practical stability criterion and the use of matrices in the Benrejeb arrow form are dev...

This paper introduces a new approach to the uniform practical stability theory of descriptor systems with infinite time delays in terms of two measurements. An easy-to-test criterion of uniform practical stability is given via Lyapunov functionals and Razumikhin technique. Finally, the application of the results obtained is demonstrated through an analysis of a class of descriptor systems with ...

The goal of this paper is twofold. The first part presents a Lyapunov statement and proof of the concept of robust global practical exponential stability (RpGES) for nonlinear time varying systems. A RpGES-Lyapunov function for the overall system is exhibited. Its proof is a consequence of some results on converse Lyapunov theorems obtained by Tsinias in [19]. The second part provides sufficien...

In this chapter we present a controlling method which allows the preservation of transient chaotic evolution in the desired region of the phase space. The concept of practical stability for the perturbed chaotic attractors and the connection between practical and asymptotic stability is described. Our controlling procedure allows asymptotically unstable chaotic attractors to become practically ...

A subset A of the state space is called uniformly globally weakly attractive if for any neighborhood S of A and any bounded subset B there is a uniform finite time τ so that any trajectory starting in B intersects S within the time not larger than τ . We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attracti...