"Poly-quadratic Stability in D-CPWL Approach for a Class of Nonlinear Systems"

In this paper, we consider nonlinear discrete time systems modeled with polytopic uncertain linear systems. We develop the CPWL (Canonical Piecewise Linear) approach proposed by Labit [1] to the case of discrete time systems associated with the new discrete time stability condition proposed by de Oliviera [2] then improved by Daafouz [3]. The obtained linear matrix inequalities condition leads to necessary and sufficient, and less conservative control design condition. This method (Discrete time -CPWL approach and poly-quadratic stability) takes also advantages of the systematic design of robust controllers in one shot and the insuring scheduling for the nonlinear discrete time system control.