Bounded Nash type controls for uncertain linear systems

This paper deals with multicriteria controls for systems coping with polytopic uncertainties. The proposed controls are inspired by a Nash strategy for exactly known systems, reformulated as a nonconvex coupling between Semi-Definite Programming problems. The extension to the uncertain case duplicates the Linear Matrix Inequalities for all vertices of the polytope. A new iterative algorithm using Semi-Definite Programming is provided to design bounded Nash type controls for uncertain systems. A numerical example is given to illustrate the design method.