This paper deals with the asymptotic stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Based on the Lyapunov–Krasovskii functional including the triple integral terms and free weighting matrices approach, a novel delay-decomposition stability criterion is obtained. The main idea of the proposed method is to divide each delay interval into two equal segment...

A novel method based on Lyapunov-Krasovskii functionals for the stability analysis of linear systems with constant is introduced. The Lyapunov-Krasovskii functionals are provided using polynomial parameters. Stability conditions are derived in the form of linear matrix inequalities. Examples show that these computationally tractable conditions can give tighter stability results than the ones in...

In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

This paper presents an original practical criterion of global stability analysis of nonlinear polynomial systems. This criterion derived from the application of the Lyapunov direct method with a quadratic function generalizes the famous Lyapunov stability condition for linear systems. Useful mathematical transformations have allowed the formulation of the obtained conditions as an LMI (Linear M...

The issue of the robust exponential passivity analysis for uncertain neutral-type neural networks with mixed interval time-varying delays is discussed in this work. For our purpose, lower bounds are allowed to be either positive or zero adopting combination model transformation, various inequalities, reciprocally convex combination, and suitable Lyapunov–Krasovskii functional. A new criterion r...

We discuss a variation of dilated matrix inequalities for the conventional Bounded Real matrix inequality, and other similarly structured inequalities. Here, system matrices are separated from Lyapunov matrix to allow the use of different Lyapunov matrices in multiobjective and robust problems. The search involves a bounded scalar parameter that enters the problem nonlinearly, and is dealt with...

This paper presents stability analysis and robust H∞ control for nonlinear switched systems bounded in sectors with arbitrary boundaries. By proposing new and more general multiple Lyapunov functions that incorporate nonlinearities in the system, we formulate the stability conditions under arbitrary switching in the form of linear matrix inequalities. Moreover, an optimization problem subject t...

This paper studies the problem of regional stability and performance analysis for a class of nonlinear uncertain systems. Both continuous-time and discrete-time systems are considered. Our approach is based on the use of polynomial Lyapunov functions. We show how these functions can be used to reduce the conservatism in analysis. The conditions for analysis are given in terms of linear matrix i...