This note deals with the robust stability analysis for time-delay systems with nonlinear perturbations. Firstly, a new class of Lyapunov functional candidate is proposed to develop some new criteria by considering the additional useful terms and introducing some freeweighting matrices. Then, an augmented Lyapunov functional is introduced to establish a novel improved stability condition. All re...

We derive the expression for a general element of an SO(n) matrix. All elements are obtained from a single element of the matrix. This has applications in recently developed methods for computing Lyapunov exponents. 1. Introduction. Matrix representations of the SO(n) group have played an important role in mathematical physics [5, 6]. They continue to be used in many fields to this day [4, 7, 8...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it ...

The exponential synchronization for a class of discrete-time uncertain complex networks with stochastic effects and time delay is investigated by using the Lyapunov stability theory and discrete Halanay inequality. The uncertainty arises from the difference of the nodes’ reliability in the complex network. Through constructing an appropriate Lyapunov function and applying inequality technique, ...

This paper presents an alternative approach for obtaining a converse Lyapunov theorem for discrete-time systems. The proposed approach is constructive, as it provides an explicit Lyapunov function. The developed converse Lyapunov theorem establishes existence of global Lyapunov functions for globally exponentially stable (GES) systems and for globally asymptotically stable systems, Lyapunov fun...