Quadratic Lyapunov function for stochastic mechanical systems with switching impacts

Autor:	Svetlana Anulova
Rok vydání:	2015
Předmět:	Lyapunov function Lyapunov optimization Lyapunov exponent symbols.namesake Wiener process Control and Systems Engineering Control theory Ordinary differential equation symbols Lyapunov equation Electrical and Electronic Engineering Lyapunov redesign Control-Lyapunov function Mathematics
Zdroj:	Automation and Remote Control. 76:1765-1770
ISSN:	1608-3032 0005-1179
DOI:	10.1134/s0005117915100045
Popis:	A general class of stochastic mechanical systems (including closed-loop control ones) developing under impacts generating both jumps and switchings is considered. We establish existence of a quadratic Lyapunov function for a system of this class: provided that the corresponding switching systems of ordinary differential equations have a common quadratic Lyapunov function and stochastic actions supplemented to them are moderate, this ordinary Lyapunov function is also a Lyapunov function for the system. Parameters of stochastic actions must satisfy the following constraints: disturbances in the force field are wiener processes with constant matrix coefficients; for jumps a certain combination of their distributions and of impacts arrival intensities is bounded relative to the ordinary common Lyapunov function. Systems of the class may have discontinuous coefficients and impacts arrival intensities; both are allowed to be time and state dependent.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c118b361b3b2fc9593a57d45aba0ab06 https://doi.org/10.1134/s0005117915100045 Zobrazit plný text záznamu Plný text ve formátu PDF