Stochastic Stabilization of Itô Stochastic Systems with Markov Jumping and Linear Fractional Uncertainty

Abstract

For a class of Itô stochastic linear systems with the Markov jumping and linear fractional uncertainty, the stochastic stabilization problem is investigated via state feedback and dynamic output feedback, respectively. In order to guarantee the stochastic stability of such uncertain systems, state feedback and dynamic output control law are, respectively, designed by using multiple Lyapunov function technique and LMI approach. Finally, two numerical examples are presented to illustrate our results.

Optimal Control of Stochastic Dynamic Systems of a Random Structure with Poisson Switches and Markov Switching

“…Systems with Markov parameters belong to an important class of systems describing processes of the rapid changes in states that occur in many cases, for example, in industry, in queuing systems [1], in ecological systems [2], in economics and finance, and in modeling of a microgrid [3]. ese systems are mathematical models of the hybrid dynamic systems, in which one part of the variables changes continuously and the other part changes discretely.…”

“…In [2], the optimal control problem for the Ito linear stochastic system with the uncertainty of the following form is solved: _ x(t) � (A(ξ(t)) + ΔA(ξ(t))x(t)) +(B(ξ(t)) + ΔB(ξ(t))u(t)) + C(ξ(t))x(t)w(t), t ≥ 0, x(0) � x 0 , ξ(0) � ξ 0 .…”