Stabilization of linear systems constrained by algebraic equations

We study the stabilization problem of linear systems with state algebraic-equation constraint. We show that this problem reduces to a constrained stabilization problem, which requires the stability of the closed-loop system and simultaneous satisfaction of a pure matrix algebraic equation in terms of the feedback gain. We provide a necessary and sufficient condition for the existence of the solution to this new constrained stabilization problem and outline a simple method for its solution. The condition for the existence of a controller with complete eigenvalue assignability is also discussed. Finally, the problem of observer for linear systems with algebraic equation constraint is formulated and solved