Regularizability of descriptor systems

Abstract

For feedback control of linear systems in descriptor form it is essential that the closed-loop system be regular; that is, there should not be an infinity of solutions of the closed-loop differential equations for any initial condition. Closed-loop regularity cannot be taken for granted. In this paper a necessaryand sufficient condition for the existence of an output feedback giving closed-loop regularity is presented.

Generalized regularity and regularizability of rectangular descriptor systems

“…Although regularization of square descriptor systems has been researched by many authors, the case of rectangular descriptor systems has not been investigated in detail. The results in [5] are also valid for rectangular descriptor systems, but the author only considered output feedback and did not give the form of regularizing feedback controllers. The purpose of this paper is to give the definition of generalized regularity for rectangular descriptor systems and present necessary and sufficient conditions for generalized regularizability under different feedback forms.…”

“…It is easy to see the definition of generalized regularity is a natural expansion of regularity. Reference [5] could first give a similar statement for generalized regularity, namely, the system has the uniqueness regularity property if the solution is unique whenever it exists. But it is easy to see that the statement in reference [5] is in the time domain with an assumption that a solution exists.…”

“…Reference [5] could first give a similar statement for generalized regularity, namely, the system has the uniqueness regularity property if the solution is unique whenever it exists. But it is easy to see that the statement in reference [5] is in the time domain with an assumption that a solution exists. Here the admissible pair (Ex(0 − ), u) guarantees the existence of solution in the frequency domain.…”

“…Definition 3 The rectangular descriptor system (1) is said to be generalized regularizable via an output plus partial state derivative feedback if the closed-loop system (5) or…”

“…Reference [4] treated the state feedback case and presented several necessary and sufficient conditions for the problem. In [5], regularization of descriptor systems via proportional output feedback was considered. In 1999, Chu and Ho [6] considered regularization of a descriptor system using proportional plus derivative output feedback and established necessary and sufficient conditions.…”