Induced L/sub 2/-norm control for LPV system with bounded parameter variation rates

A linear, finite-dimensional plant, with state-space parameter dependence, is controlled using a parameter-dependent controller. The parameters whose values are in a compact set, are known in real time. Their rates of variation are bounded and known in real time also. The goal of control is to stabilize the parameter-dependent closed-loop system, and provide disturbance/error attenuation as measured in induced L/sub 2/ norm. The authors' approach uses a parameter-dependent Lyapunov function, and solves the control synthesis problem by reformulating the existence conditions into an semi-infinite dimensional convex optimization. The authors propose finite dimensional approximations to get sufficient conditions for successful controller design.

[1]  G. Meyer,et al.  Application of Nonlinear Systems Inverses to Automatic Flight Control Design: System Concepts and Flight Evaluations , 1981 .

[2]  Eduardo Sontag,et al.  On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[3]  Pramod P. Khargonekar,et al.  On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings , 1981, CDC 1981.

[4]  Pramod P. Khargonekar,et al.  On the control of linear systems whose coefficients are functions of parameters , 1984 .

[5]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

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

[7]  P. Khargonekar,et al.  The H/sup infinity / control problem for linear time-varying systems , 1990, 29th IEEE Conference on Decision and Control.

[8]  Gilead Tadmor,et al.  Worst-case design in the time domain: The maximum principle and the standardH∞ problem , 1990, Math. Control. Signals Syst..

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

[10]  Wilson J. Rugh,et al.  Analytical Framework for Gain Scheduling , 1990, 1990 American Control Conference.

[11]  Michael Athans,et al.  Analysis of gain scheduled control for nonlinear plants , 1990 .

[12]  S. M. Shahruz,et al.  Design of controllers for linear parameter-varying systems by the gain scheduling technique , 1990, 29th IEEE Conference on Decision and Control.

[13]  Gain Scheduling: Potential Hazards and Possible Remedies , 1992, 1991 American Control Conference.

[14]  J. Doyle,et al.  Stabilization of LFT systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[15]  A. Packard,et al.  A collection of robust control problems leading to LMIs , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[16]  Carsten W. Scherer,et al.  H∞ -optimization without assumptions on finite or infinite zeros , 1992 .

[17]  D. Bernstein,et al.  Extensions of mixed- mu bounds to monotonic and odd monotonic nonlinearities using absolute stability theory. I , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[18]  B. Anderson,et al.  A game theoretic approach to H ∞ control for time-varying systems , 1992 .

[19]  J. Doyle,et al.  H/sub infinity / control of LFT systems: an LMI approach , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[20]  S. Behtash,et al.  Design of controllers for linear parameter-varying systems by the gain scheduling technique , 1992 .

[21]  Keith Glover,et al.  The application of scheduled H∞ controllers to a VSTOL aircraft , 1993, IEEE Trans. Autom. Control..

[22]  Pierre Apkarian,et al.  A convex characterization of parameter-dependent H/sub /spl infin// controllers , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[23]  Stephen P. Boyd,et al.  Method of centers for minimizing generalized eigenvalues , 1993, Linear Algebra and its Applications.

[24]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

[25]  A. Packard.  Gain scheduling via linear fractional transformations , 1994 .

[26]  Dennis S. Bernstein,et al.  Extensions of mixed-µ bounds to monotonic and odd monotonic nonlinearities using absolute stability theory† , 1994 .

[27]  M. Overton,et al.  Optimizing eigenvalues of symmetric definite pencils , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[28]  Tetsuya Iwasaki,et al.  All controllers for the general H∞ control problem: LMI existence conditions and state space formulas , 1994, Autom..

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

[30]  J. Doyle,et al.  𝓗∞ Control of Nonlinear Systems: a Convex Characterization , 1995, IEEE Trans. Autom. Control..

[31]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[32]  Arkadi Nemirovski,et al.  The projective method for solving linear matrix inequalities , 1997, Math. Program..