Gain-scheduled H∞-control of discrete-time polytopic time-varying systems

This paper presents synthesis procedures for the design of both robust and gain-scheduled H∞ static output feedback controllers for discrete-time linear systems with time-varying parameters. The parameters are assumed to vary inside a polytope and have known bounds on their rate of variation. The geometric properties of the polytopic domain are exploited to derive a finite set of linear matrix inequalities that consider the bounds on the rate of variation of the parameters. A numerical example illustrates the proposed approach.

[1]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[2]  W. Xie.  H2 gain scheduled state feedback for LPV system with new LMI formulation , 2005 .

[3]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[4]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[5]  Valter J. S. Leite,et al.  Gain scheduled state feedback control of discrete-time systems with time-varying uncertainties: an LMI approach , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[6]  J. Geromel,et al.  Convex analysis of output feedback control problems: robust stability and performance , 1996, IEEE Trans. Autom. Control..

[7]  Pierre Apkarian,et al.  Advanced gain-scheduling techniques for uncertain systems , 1998, IEEE Trans. Control. Syst. Technol..

[8]  P.L.D. Peres,et al.  Robust stability analysis and control design for time-varying discrete-time polytopic systems with bounded parameter variation , 2008, 2008 American Control Conference.

[9]  Michael Athans,et al.  Guaranteed properties of gain scheduled control for linear parameter-varying plants , 1991, Autom..

[10]  Jamal Daafouz,et al.  Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties , 2001, Syst. Control. Lett..

[11]  J. Geromel,et al.  Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems , 2002 .

[12]  Ian Postlethwaite,et al.  Scheduling schemes for an integrated flight and propulsion control system , 2002 .

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

[14]  Ricardo C. L. F. Oliveira,et al.  LMI approach for H linear parameter-varying state feedback control , 2005 .

[15]  Ricardo C. L. F. Oliveira,et al.  Linear matrix inequality characterisation for H ∞ and H 2 guaranteed cost gain-scheduling quadratic stabilisation of linear time-varying polytopic systems , 2007 .

[16]  Carlos E. de Souza,et al.  Robust /spl Hscr//sub /spl infin// filtering for discrete-time linear systems with uncertain time-varying parameters , 2006, IEEE Transactions on Signal Processing.

[17]  Sérgio Ricardo de Souza,et al.  H/sub 2/ output feedback control for discrete-time systems , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[18]  Jan Swevers,et al.  AN APPLICATION OF INTERPOLATING GAIN-SCHEDULING CONTROL , 2007 .

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

[20]  P.L.D. Peres,et al.  Design of H∞ Gain-Scheduled Controllers for Linear Time-Varying Systems by means of Polynomial Lyapunov Functions , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[21]  C. de Souza,et al.  Gain‐scheduled ℋ︁2 controller synthesis for linear parameter varying systems via parameter‐dependent Lyapunov functions , 2006 .

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

[23]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[24]  Massimiliano Mattei,et al.  Gain scheduled control for discrete‐time systems depending on bounded rate parameters , 2005 .

[25]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[26]  Fen Wu,et al.  Induced L2‐norm control for LPV systems with bounded parameter variation rates , 1996 .

[27]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[28]  Wilson J. Rugh,et al.  Gain scheduling for H-infinity controllers: a flight control example , 1993, IEEE Trans. Control. Syst. Technol..

[29]  Valter J. S. Leite,et al.  Robust control through piecewise Lyapunov functions for discrete time-varying uncertain systems , 2004 .

[30]  Laurent El Ghaoui,et al.  Advances in linear matrix inequality methods in control: advances in design and control , 1999 .

[31]  Karina A. Barbosa,et al.  Robust /spl Hscr//sub 2/ filtering for discrete-time uncertain linear systems using parameter-dependent Lyapunov functions , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

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

[33]  Jan Swevers,et al.  Identification of MIMO LPV models based on interpolation , 2008 .

[34]  M. Athans,et al.  Gain Scheduling: Potential Hazards and Possible Remedies , 1992, 1991 American Control Conference.

[35]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[36]  Carsten W. Scherer,et al.  LPV control and full block multipliers , 2001, Autom..

[37]  A. Stoorvogel.  The robust H2 control problem: a worst-case design , 1993, IEEE Trans. Autom. Control..

[38]  William Leithead,et al.  Survey of gain-scheduling analysis and design , 2000 .

[39]  Massimiliano Mattei,et al.  Gain Scheduled Control for Discrete-Time Systems Depending on Bounded Rate Parameters , 2000 .