Exponential stability of nonlinear discrete 2D systems

The paper develops the method of vector Lyapunov function as a unified approach to stability analysis of nonlinear discrete-time 2D systems. We derive sufficient conditions of exponential stability for nonlinear Fornasini-Marchesini systems and sufficient conditions of pass profile exponential stability for nonlinear repetitive processes. These results are extended to the nonlinear repetitive processes with random failures modeled by Markov chain with finite set of states. In the linear case these conditions are expressed in the form of linear matrix inequalities. Finally, we describe an application to iterative learning control design for the simplest model of gantry robot under information failures.