Stability and Stabilization of Nonlinear 2D Markovian Jump Systems with Applications

Abstract

This paper develops a vector Lyapunov function based approach to the stability of continuous and discrete 2D nonlinear systems with Markovian jumps. Nonlinear continuous-time 2D systems described by a Roesser model and nonlinear discrete-time repetitive process with Markovian jumps are considered, for which global asymptotic stability in the mean square is defined and sufficient conditions for the existence of this property obtained in terms of stochastic vector Lyapunov functions. These conditions are then applied to iterative learning control design for a set of linear systems with jumps that are controlled over a network. The resulting networked ILC model has the form of repetitive process with a Markovian random structure. The ILC convergence problem is reduced to a stochastic stabilization problem, where the use of a stochastic Lyapunov function as a vector of quadratic forms results in control law design algorithms that can be computed using linear matrix inequalities.