Constrained stabilization problem and transient mismatch phenomena in singularly perturbed systems

We study the stabilization of a linear system by a state feedback whose gain matrix satisfies a certain constraint. We show that the problem can be converted to an equivalent stabilization problem by a static output feedback where the static gain takes a special structure. The application of this result to the design of an observer based controller for singularly perturbed systems is discussed. It is shown that the transient mismatch phenomena associated with this type of design may be alleviated if the observer gain of the fast observer is chosen based on the solution of a certain constrained stabilization problem.