Improved Stability Criteria on Linear Systems with Distributed Interval Time-Varying Delays and Nonlinear Perturbations

The problem of delay-range-dependent stability analysis for linear systems with distributed time-varying delays and nonlinear perturbations is studied without using the model transformation and delay-decomposition approach. The less conservative stability criteria are obtained for the systems by constructing a new augmented Lyapunov–Krasovskii functional and various inequalities, which are presented in terms of linear matrix inequalities (LMIs). Four numerical examples are demonstrated for the results given to illustrate the effectiveness and improvement over other methods.

A Novel Stability Criterion of Lur’e Systems with Time-Varying Delay Based on Relaxed Conditions

This paper considers the absolute stability for Lur’e systems with time-varying delay and sector-bounded nonlinear. In this paper, a new relaxed condition based on delay decomposition approach is proposed. By using this technique and employing some inequality, the new delay-dependent stability criteria for Lur’e systems are derived in the form of linear matrix inequalities (LMIs). A numerical example is presented to show less conservatism of proposed methods compared with the previous.

A New Integral Inequality and Delay-Decomposition with Uncertain Parameter Approach to the Stability Analysis of Time-Delay Systems

This paper is concerned with the problem of delay-dependent stability of time-delay systems. Firstly, it introduces a new useful integral inequality which has been proved to be less conservative than the previous inequalities. Next, the inequality combines delay-decomposition approach with uncertain parameters applied to time-delay systems, based on the new Lyapunov-Krasovskii functionals and new stability criteria for system with time-delay have been derived and expressed in terms of LMIs. Finally, a numerical example is provided to show the effectiveness and the less conservative feature of the proposed method compared with some recent results.