Simultaneous H∞ control for a class of linear uncertain systems :: An LMI approach

The problem of simultaneous H-infinity control for a class of linear systems with norm-bounded uncertainties is investigated. I 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 disturbance attenuation level. Via the linear matrix inequality (LMI) technique, the problem can be converted to a corresponding convex optimization algorithm which subject to multiple LMIs constraints. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.