A GEOMETRIC APPROACH TO OPTIMAL STATE-SPACE SOLUTIONS WITH MINIMAL REALIZATION FOR STANDARD DISCRETE-TIME H-2 CONTROL PROBLEM

作者：Wu Po Feng; Wang Pei Ju; Yung Chee Fai^*

来源：Journal of the Chinese Institute of Engineers, 2010, 33(3): 429-435.

DOI：10.1080/02533839.2010.9671631

• minimal realization
• H-2 control
• algebraic Riccati equations
• geometric approach
• Lyapunov equations

This paper shows that the controllable and unobservable subspaces of the discrete-time H-2 optimal controller can be characterized by the image and kernel spaces of two matrices Z(2) and W-2, where Z(2) and W-2 are positive semi-definite solutions of two pertinent Lyapunov equations whose coefficients involve the stabilizing solutions of two celebrated discrete-time algebraic Riccati equations (DAREs) used in solving the H-2 optimal control problem. By suitably choosing the bases adapted to Z(2) and W-2, a minimal order state-space realization of an H-2 optimal controller is then given via an elegant geometric approach. In terms of geometric language, all the results and proofs given are clear and simple.

• 出版日期2010-4