Improved delay-range-dependent stability analysis of a time-delay system with norm bounded uncertainty

Further results on stabilization for interval time-delay systems via new integral inequality approach

This paper investigates the stability and stabilization problems for interval time-delay systems. By introducing a new delay partitioning approach, various Lyapunov-Krasovskii functionals with triple-integral terms are established to make full use of system information. In order to reduce the conservatism, improved integral inequalities are developed for estimation of double integrals, which show remarkable outperformance over the Jensen and Wirtinger ones. Particularly, the relationship between the time-delay and each subinterval is taken into consideration. The resulting stability criteria are less conservative than some recent methods. Based on the derived condition, the state-feedback controller design approach is also given. Finally, the numerical examples and the application to inverted pendulum system are provided to illustrate the effectiveness of the proposed approaches.

Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties

This paper addresses the dynamics of a class of discrete-time switched nonlinear systems with time-varying delays and uncertainties and subject to perturbations. It is assumed that the nominal switched nonlinear system is robustly uniformly exponentially stable. It is revealed that there exists a maximal Lipschitz constant, if perturbation satisfies a Lipschitz condition with any Lipschitz constant less than the maximum, then the perturbed system can preserve the stability property of the nominal system. In situations where the perturbations are known, it is proved that there exists an upper bound of coefficient such that the perturbed system remains exponentially stable provided that the perturbation is scaled by any coefficient bounded by the upper bound. A numerical example is provided to illustrate the proposed theoretical results.