Absolute stability and stabilization of 2D Roesser systems with nonlinear output feedback

This paper considers 2D systems described by the discrete Roesser model with linear dynamics in the forward path and a feedback path containing a memoryless, possibly time-varying, nonlinearity. Based on the extension of absolute stability theory to this class of systems, sufficient conditions for absolute p-stability are obtained and for the particular case of p = 2 linear matrix inequality based tests for this property are obtained, together with an algorithm to design a stabilizing nonlinear control law. The extension of these results to 2D discrete systems described by the Roesser model with Markovian jumps is also given. A numerical example to demonstrate the applicability and effectiveness of these new results concludes the paper.