Analysis and control of polytopic uncertain/nonlinear systems in the presence of bounded disturbance inputs

For a general input-output system subjected to disturbance inputs whose magnitudes are uniformly bounded, we introduce the notion of L_∞ stability with level of performance γ. We present a sufficient condition which guarantees L_∞ stability of this system. Furthermore, for a specific class of uncertain/nonlinear systems, characterized by a polytopic condition, this condition results in a bunch of matrix inequalities. An iterative algorithm based on LMIs (linear matrix inequalities) is proposed for minimizing the level of performance. We also investigate the use of linear state feedback controllers to minimize the level of performance and illustrate our results with a nontrivial example