OPTIMAL QUADRATIC STABILIZABILITY OF UNCERTAIN LINEAR SYSTEMS.

The problem of stabilizing uncertain linear systems is addressed. The uncertainty, q( multiplied by (times) ), which enters the system dynamics lacks a statistical description. Instead, the uncertainty is described via a set Q which serves as a bound for the admissible variations of q( multiplied by (times) ). The results given differ from previous work in the following manner: the uncertain system parameters are not restricted by the so-called ″matching conditions″ ; nor do we enforce (possibly conservative) bounds on the uncertainty. Instead, the problem of stabilization is reformulated as a search for an ″optimal″ quadratic Lyapunov function. Such an approach leads to criteria which are necessary and sufficient for quadratic stabilizability. The efficacy of this method is demonstrated by an example which cannot be handled by the theory developed to date.