On LQ Control Problem for Linear Discrete-Time Systems with Singular Weightings

Abstract

In this paper, we discuss the LQ problem for discrete-time linear systems with singular weightings. The interactor with all-pass property is used to properize a given strictly proper system. In our approach, the type of Riccati equation to be solved is different from the result for a square trasfer function matrix case. The relation between our approach and the former result is discussed. Unlike the square case, the explicit solution to the problem cannot be obtained and a recursive method to solve the Riccati equation is shown. An application to the finite settling-time control is also discussed.