Inclusion principle for uncertain discrete-time systems with guaranteed cost

Abstract

The paper presents an extension of the inclusion principle to uncertain nominally linear discrete-time systems with quadratic costs using the concept of quadratic guaranteed cost control. The uncertainty is assumed to be time-varying norm-bounded in both state and input matrices. The main contribution is the derivation of conditions under which a quadratic guaranteed cost control designed in the expanded space can be contracted to the initial system preserving simultaneously the value of the cost functions. The control law is designed in the expanded space by using an LMI approach. The specialization of the results on feedback control with decentralized information structure constraints is given. An illustrative example is supplied.