Output feedback disk pole assignment for systems with positive real uncertainty

In this paper, the problem of pole assignment in a disk by output feedback for continuous or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given. Some related problems are also discussed.

[1]  A. Laub,et al.  On the numerical solution of the discrete-time algebraic Riccati equation , 1980 .

[2]  E. Noldus.  Design of robust state feedback laws , 1982 .

[3]  Sang Bong Kim,et al.  Pole assignment in a specified disk , 1987 .

[4]  Mitsuji Sampei,et al.  An algebraic approach to H ∞ output feedback control problems , 1990 .

[5]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[6]  S. Bittanti,et al.  The Riccati equation , 1991 .

[7]  D. Bernstein,et al.  Robust stabilization with positive real uncertainty: beyond the small gain theory , 1991 .

[8]  D. Bernstein,et al.  Controller design with regional pole constraints , 1992 .

[9]  D. Bernstein,et al.  Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory , 1993 .

[10]  Denis Arzelier,et al.  Pole assignment of linear uncertain systems in a sector via a Lyapunov-type approach , 1993, IEEE Trans. Autom. Control..

[11]  D. Shim.  Quadratic stability and the positivity theorem or circle theorem , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[13]  Germain Garcia,et al.  Pole assignment for uncertain systems in a specified disk by output feedback , 1996, Math. Control. Signals Syst..