One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters

Taras Lukashiv

doi:10.1155/2016/1694935

Abstract

The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained.

Highlights

The explicit view of the Lyapunov operator is necessary for solving the problem of stabilization for stochastic dynamic systems
The explicit view of infinitesimal operator for the solution of dynamic systems of random structure with Markov switching and constant delay is obtained in this article
The weak infinitesimal operator Q on solutions of system (1)–(3) of functional U is calculated by the formula (QU) (t, y, h, φ) = (LtU) (t, y, h, φ)

Summary

Introduction

The explicit view of the Lyapunov operator is necessary for solving the problem of stabilization for stochastic dynamic systems. The view of the Lyapunov operator for different stabilization problems can be found in [1,2,3,4,5,6,7]. In [6], the view of the Lyapunov operator for stochastic diffusion dynamical system of random structure with Markov switching is obtained, in [7], for controlled stochastic dynamical system with impulse Markov switching and parameters. The explicit view of infinitesimal operator (of Lyapunov type) for the solution of dynamic systems of random structure with Markov switching and constant delay is obtained in this article

Formulation of the Problem

Calculation Infinitesimal Operator

Model Example

Conclusion