Robust control with adaptive compensation input for linear uncertain systems

This paper deals with a design problem of a robust controller which achieves not only robust stability but also a performance robustness for linear systems with structured uncertainties satisfying matching condition. The performance robustness means that comparing the transient behavior of the uncertain system with a desired one generated by the nominal system, the deterioration of control performance is suppressed. In this approach, the control law consists of a state feedback with the fixed gain designed by using the nominal system, a state feedback with an adaptive gain determined by a parameter adjustment law and a compensation input for the purpose of keeping transient behavior as closely as possible to the desirable one. We show the parameter adjustment law in order to guarantee robust stability and that the condition for the existence of the compensation input is equivalent to the Riccati equation for the standard linear quadratic control problem. Finally, numerical examples are presented.