Towards Less Conservative Stability Criterion for Discrete-Time Linear Uncertain Systems

The stability problem of discrete-time linear uncertain systems is considered. The uncertainty is expressed in terms of uncertain system matrix, and is allowed to be arbitrary time varying. The criterion is based on quadratic stability. The necessary and sufficient condition of the quadratic stability is formulated in a two level optimization problem. The higher level of this optimization is proved to be convex. When the uncertainty bounding set is a hyperpolyhedron, the lower level can be reached by one of the finite number of vertices. An illustrative example is presented to show the advantage of the proposed criterion.