Optimal control of Volterra type stochastic difference equations

AbstractMany processes in automatic regulation, physics, etc. can be modelled by stochastic difference equations. One of the main problems of the theory of difference equations and their applications is connected with stability and optimal control [1]. In this paper we discuss the optimal control of second-kind Volterra type stochastic difference equations. In [2–9] for Volterra type stochastic integral equations, analogous results were obtained

Generalised criteria on delay dependent stability of highly nonlinear hybrid stochastic systems

Our recent paper [2] is the first to establish delay dependent criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) (by highly nonlinear we mean the coefficients of the SDDEs do not have to satisfy the linear growth condition). This is an important breakthrough in the stability study as all existing delay stability criteria before could only be applied to delay equations where their coefficients are either linear or nonlin- ear but bounded by linear functions (namely, satisfy the linear growth condition). In this continuation, we will point out one restrictive condition imposed in our earlier paper [2]. We will then develop our ideas and methods there in order to remove this restrictive condition so that our improved results cover a much wider class of hybrid SDDEs

Stability of difference analogue of linear mathematical inverted pendulum

A sufficient condition to preserve the property of asymptotic stability for a difference analogue of the linear mathematical inverted pendulum is obtained

Application of the general methods of Lyapunov functionals construction for Volterra difference equations

Abstract: Lyapunov functionals are used usually for stability investigation of systems with aftereffect. The general method of Lyapunov functionals construction which was proposed and developed by Kolmanovskii and Shaikhet is used here for stochastic second type Volterra difference equations. It is shown that using this method, there is a possibility to construct for a given equation, a sequence of extending stability regions. Keywords: Difference equations, Method of Lyapunov functionals construction, Asymptotic stability. 1. STATEMEN