On the Solvability of the Constrained Lyapunov Problem

This paper considers system theoretic conditions for the solvability of the so-called constrained Lyapunov problem for nonsquare systems. These problems commonly appear in the control systems literature. Both a static output feedback problem and an observer problem are considered. The basis for the work described in this paper is a new canonical form that simplifies the analysis and deals with the equality constraint in a simple way.