Observer-based robust control giving consideration to transient behavior for linear systems with structured uncertainties

In this paper, we present an observer-based robust controller design method which achieves performance robustness together with robust stability for linear multivariable systems with structured uncertainties. 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 and at the same time excessive control input is avoided. In this approach, we assume that the control law consists of a state feedback law for the nominal system and a compensation input in order to prevent the error between the transient behavior for the uncertain system and the desired one. The compensation input is additional modification term given by feedback form of an estimated error signal and is determined so that an upper bound on a quadratic cost function of the augmented error system is minimized. We show that a condition for the existence of the compensation input which minimizes an upper bound of the quadratic cost function for the error system is given in terms of linear matrix inequalities (LMIs). Finally, numerical examples are presented.