Guaranteed cost analysis and control for a class of uncertain nonlinear discrete-time systems

This paper deals with the problem of guaranteed cost analysis and control of a class of nonlinear discrete-time systems with uncertain parameters. We use polynomial Lyapunov functions to derive stability conditions with a guaranteed bound on the 2-norm of the performance output in terms of linear matrix inequalities (LMIs). We then extend this approach to the control design by considering parameter-dependent Lyapunov functions and nonlinear (stateand parameter-dependent) multipliers.