Optimal Control for Linear Descriptor Systems

Abstract

The quadratic optimal control problem is investigated for linear descriptor systems which are the natural models of various practical control systems such as circuits systems, economics, power systems, robots and electric networks, etc. First by adopting restricted system transformation (RST), a type of generalized Lyapunov equation is proposed to study the asymptotic stability of the descriptor systems concerned. Then based on this Lyapunov equation, a generalized Riccati equation is derived and studied. Finally several necessary and sufficient conditions for the existence of optimal controller are obtained by using this Riccati equation and the optimal controller guarantees that the pre specified performance index is obtained as well as the asymptotic stability of the closed loop systems. The result here shows that it is unnecessary to consider the impulse behaviors when one wants only to discuss the asymptotic stability and the quadratic optimal control problem of the linear descriptor systems.OptimalCon