Simultaneous Guaranteed Cost Control for A Class of Linear Uncertain Systems: An LMI Approach

The problem of simultaneous guaranteed cost control for a class of linear systems with norm-bounded uncertainties is investigated. Using the concept of simultaneous Lyapunov functions, we synthesize a state-feedback control law to stabilize the class of uncertain systems simultaneously, and at the same time, minimize the upper bound of quadratic cost function. Based on the linear matrix inequality (LMI) technique, we convert the problem to a corresponding convex optimization algorithm which subject to multiple LMIs constraints. Finally, we give a numerical example to illustrate the effectiveness of our approach.