Positive real /spl Hscr//sub /spl infin// controller design-an LMI approach

This paper presents a solution to the /spl Hscr//sub /spl infin// control problem for an extended strictly positive real plant subject to the constraint that the controller is positive real. Under a fixed order approximation of an /spl Rscr//spl Hscr//sub /spl infin// parameter, a necessary and sufficient condition is given in terms of a system of linear matrix inequalities. A flexible beam example is included to illustrate the design methodology.

[1]  Vasile Mihai Popov,et al.  Hyperstability of Control Systems , 1973 .

[2]  J. Wen,et al.  Asymptotically stable set point control laws for flexible robots , 1992 .

[3]  D. S. Bernstein,et al.  Robust stabilization with positive real uncertainty: beyond the small gain theorem , 1990, 29th IEEE Conference on Decision and Control.

[4]  Dennis S. Bernstein,et al.  Design of strictly positive real, fixed-order dynamic compensators , 1990, 29th IEEE Conference on Decision and Control.

[5]  Pramod P. Khargonekar,et al.  Controller Synthesis to Render a Closed Loop Transfer Function Positive Real , 1993, 1993 American Control Conference.

[6]  R. Lozano-Leal,et al.  On the design of the dissipative LQG-type controllers , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[7]  John T. Wen,et al.  Positive real controller design with H/sub /spl infin// norm performance bound , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[8]  M. Safonov,et al.  Synthesis of positive real multivariable feedback systems , 1987 .

[9]  K. Goh,et al.  Control system synthesis via bilinear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[10]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[11]  K. Glover,et al.  A characterization of all solutions to the four block general distance problem , 1991 .

[12]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .

[13]  Stephen P. Boyd,et al.  Linear controller design: limits of performance , 1991 .