ROBUST Hinfinity CONTROL FOR SYSTEMS WITH TIME-VARYING PARAMETER UNCERTAINTY AND VARIANCE CONSTRAINTS

In this paper, the problem of designing robust Hinfinity controllers for linear continuous-time systems subjected to time-varying parameter uncertainty and steady-state variance constraints is considered. The goal of this problem is to design the state feedback controller, such that for all admissible time-varying parameter perturbations, the steady-state variance of each state is not more than the individual prespecified upper bound and the Hinfinity norm of the transfer function from disturbance inputs to system outputs meets the prespecified upper bound constraint, simultaneously. The parameter uncertainties are allowed to be time-varying and norm-bounded. A purely algebraic matrix equation approach is effectively utilized to solve the problem addressed. The existence conditions as well as the explicit expression of desired controllers are presented, and two illustrative examples are used to demonstrate the applicability of the proposed design procedure.

[1]  Karolos M. Grigoriadis,et al.  Covariance Controllers: A New Parameterization of the Class of All Stabilizing Controllers , 1990, 1990 American Control Conference.

[2]  R. Skelton,et al.  Liapunov and Covariance Controllers , 1992, 1992 American Control Conference.

[3]  Karolos M. Grigoriadis,et al.  Multiobjective Control Design via Linear Matrix Equations , 1993 .

[4]  Zhi Guo,et al.  Eigenstructure assignment in state covariance control , 1995 .

[5]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .

[6]  R.E. Skelton.  Increased roles of linear algebra in control education , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[7]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[8]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[9]  Emmanuel G. Collins,et al.  A theory of state covariance assignment for discrete systems , 1987 .

[10]  Karolos M. Grigoriadis,et al.  Alternating convex projection methods for covariance control design , 1994 .

[11]  Karolos M. Grigoriadis,et al.  Minimum-energy covariance controllers , 1997, Autom..

[12]  Heinz Unbehauen,et al.  Robust state estimation for perturbed continuous systems with circular pole and error variance constraints , 1998 .

[13]  Wang Zidong,et al.  Controller design for continuous systems with variance and circular pole constraints , 1995 .

[14]  Karolos M. Grigoriadis,et al.  Robust regional pole assignment with output feedback , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[15]  Robert Skelton,et al.  A covariance control theory , 1985, 1985 24th IEEE Conference on Decision and Control.