Stability of nonlinear 2D systems described by the continuous-time Roesser model

This paper considers systems with two-dimensional dynamics (2D systems) described by the continuous-time nonlinear state-space Roesser model. The sufficient conditions of exponential stability in terms of vector Lyapunov functions are established. These conditions are then applied to analysis of the absolute stability of a certain class of systems comprising a linear continuous-time plant in the form of the Roesser model with a nonlinear characteristic in the feedback loop, which satisfies quadratic constraints. The absolute stability conditions are reduced to computable expressions in the form of linear matrix inequalities. The obtained results are extended to the class of continuous-time systems governed by the Roesser model with Markovian switching. The problems of absolute stability and stabilization via state- and output-feedback are solved for linear systems of the above class. The solution procedures for these problems are in the form of algorithms based on linear matrix inequalities.