Vector Lyapunov Function based Stability of a Class of Applications Relevant 2D Nonlinear Systems

Abstract

A substantial literature exists on the stability and control of 2D systems, including repetitive processes where iterative learning control algorithms designed in this setting have been experimentally verified. Most of this development has assumed that the dynamics can be adequately represented by linear state-space models, but applications exist where this assumption does not hold. This paper contributes to the development of a stability theory for nonlinear discrete-time 2D systems, where main results are on the use of vector Lyapunov functions to characterize exponential stability. The analysis includes systems where random failures modeled by a Markov chain with a finite set of states can arise in an iterative learning control application. An illustrative example is also given.