On Almost Sure Stability of Hybrid Stochastic Systems With Mode-Dependent Interval Delays

Abstract

The Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Abstract-This note develops a Razumikhin-type theorem on th moment input-to-state stability of hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), which is an improvement of an existing result. An application to hybrid stochastic delay systems verifies the effectiveness of the improved result.

Almost sure state estimation withH2-type performance constraints for nonlinear hybrid stochastic systems

“…On the other hand, the H ∞ filtering can be regarded as a suboptimal filtering due to its capability of providing a smaller bound for the worst-case estimation error [1,2]. It might be worth emphasizing that, in most of the existing results, the estimators are designed to guarantee that the dynamics of the estimation error converges in terms of certain stability concepts such as the stochastic asymptotic stability [23], the mean-square stability [6][7][8]11], the mean-square exponential stability [29], the pth moment stability [14], and the asymptotic stability in probability [24].…”

“…For example, the performance requirement of the controlled rocket should be guaranteed with the probability 1. Very recently, the analysis and design problems in almost sure sense have attracted considerable attention, see [3,4,13,14,30] and the references therein. For instance, a Razumikhin-type theorem on pth moment input-to-state stability has been developed in [14] for a class of nonlinear stochastic systems with Markovian switching.…”

“…Very recently, the analysis and design problems in almost sure sense have attracted considerable attention, see [3,4,13,14,30] and the references therein. For instance, a Razumikhin-type theorem on pth moment input-to-state stability has been developed in [14] for a class of nonlinear stochastic systems with Markovian switching. In [13], a desired controller has been designed to stabilize a stochastic system almost surely which may not be stabilized in mean-square sense.…”

Stabilisation of hybrid stochastic systems by disordered controllers

“…During the past decades, a lot of attention has been paid on this class of systems, see e.g. [11][12][13][14][15][16][17]. Especially, it has been proved that the stabilisation and destabilisation of stochastic systems can be achieved by a Brownian noise perturbation [18][19][20][21].…”

Stochastic stabilization of singular systems with Markovian switchings

“…have received a lot of attention and are widely used, see e.g., [35][36][37][38][39]. It is obtained from these references that the stabilization problem is realized by a regular controller in terms of being in the drift part.…”