Journal des systèmes électriques et électroniques

Linear Quadratic Regulator for Impulse Uncontrollable Singular Systems

Abstract

Xiaoping Liu and Yufu Jia

This paper investigates the linear quadratic regulator problem for singular systems which may contain some impulse uncontrollable modes. By transforming to the Weierstrass form, impulse controllable and uncontrollable subsystems can be separated. Sufficient conditions are proposed, under which solutions to both state and costate equations for the linear quadratic regulator problem are impulse-free. The necessary conditions for the minimization of the quadratic cost function are converted to a two-point boundary value problem, which can be solved by either computing its back-time state transition matrix or solving a Riccati equation. Two examples are provided to illustrate the main results.