H/sub 2/ output feedback control for discrete-time systems

This paper addresses the problem of H/sub 2/ control by output feedback for discrete-time systems. Necessary and sufficient conditions concerning the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real-valued function. The results can be easily extended to deal with linear uncertain discrete-time systems, where uncertainties are supposed to belong to convex bounded domains, providing an H/sub 2/ guaranteed cost output feedback control. Thanks to the geometric properties of the above mentioned function, numerical convex programming tools can be used in order to solve this class of H/sub 2/ control problems. Examples illustrate the theoretical results.

[1]  Ian R. Petersen,et al.  A procedure for simultaneously stabilizing a collection of single input linear systems using non-linear state feedback control , 1987, Autom..

[2]  Isaac Kaminer,et al.  Mixed H2/H∞ control for discrete-time systems via convex optimization , 1992, American Control Conference.

[3]  Vinicius Amaral Armentano,et al.  Structural constrained controllers for discrete-time linear systems , 1989 .

[5]  Pedro Luis Dias Peres,et al.  H2 control for discrete-time systems optimality and robustness, , 1993, Autom..

[6]  U. Shaked,et al.  A transfer function approach to the problems of discrete-time systems: H/sub infinity /-optimal linear control and filtering , 1991 .

[7]  Sérgio Ricardo de Souza,et al.  Convex analysis of output feedback structural constraints , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[8]  P. Peres,et al.  On a convex parameter space method for linear control design of uncertain systems , 1991 .

[9]  I. Yaesh,et al.  Transfer Function Approach to the Problems of Discrete-time Systems : H_∞-optimal Linear Control and Filtering , 1991 .

[10]  Lihua Xie,et al.  On the Discrete-time Bounded Real Lemma with application in the characterization of static state feedback H ∞ controllers , 1992 .

[11]  P. Makila,et al.  Computational methods for parametric LQ problems--A survey , 1987 .

[12]  Sérgio Ricardo de Souza,et al.  ℋ2 guaranteed cost control for uncertain discrete-time linear systems , 1993 .