Combined controller-observer design for uncertain systems: using necessary and sufficient conditions

The problem of stabilizing a class of linear uncertain systems by using estimated state feedback is discussed. The system possesses uncertainty which is time-varying. The uncertainty is unknown, but lies within a prescribed set (hence it is bounded). No statistical information about the uncertainty is imposed. The estimated state is constructed via an observer. Necessary and sufficient conditions for quadratic stabilizability are formulated. The controller synthesis and stability analysis are investigated by a two-level optimization process. The inner level searches for the minimum and can be achieved by checking a finite number of vertices if the bounding set is a hyperpolyhedron. The outer level can reach the global maximum. The result is believed to be practical (in the sense that it can be implemented for nontrivial physical systems) and nonconservative