The State Response and Controllability of Regular Polynomial Matrix Systems

In this paper, the problems of state response and controllability conditions for higher-order descriptor systems are analyzed. For the nonhomogeneous higher-order polynomial matrix system, the complete solutions are derived under the nonzero initial state and initial input conditions based on the Smith-MacMillan form of a rational matrix at infinity and the finite and infinite Jordan matrices of the polynomial matrix. Meanwhile, the admissible initial conditions of the system are discussed, which can avoid the system producing impulsive behavior. Finally, the controllability subspace is constructed by analyzing the proposed solution structure of the associated system equation, and algebraic criteria of controllability is given.