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 timevarying 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. © 2008 IEEE.38723877Rugh, W.J., Shamma, J.S., Research on gain scheduling (2000) Automatica, 36 (10), pp. 1401-1425Shamma, J.S., Athans, M., Guaranteed properties of gain scheduled control for linear parameter-varying plants (1991) Automatica, 27 (3), pp. 559-564Apkarian, P., Adams, R.J., Advanced gain-scheduling techniques for uncertain systems (1998) IEEE Trans. Control Syst. Technol, 6 (1), pp. 21-32Apkarian, P., Gahinet, P., Becker, G., Self-scheduled H∞, control of linear parameter-varying systems - A design example (1995) Automatica, 31 (9), pp. 1251-1261Packard, A., Gain scheduling via linear fractional transformations (1994) Syst. Contr. Lett, 22 (2), pp. 79-92Leith, D.J., Leithead, W.E., Survey of gain-scheduling analysis and design (2000) Int. J. Control, 73 (11), pp. 1001-1025Shamma, J.S., Athans, M., Gain scheduling: Potential hazards and possible remedies (1992) IEEE Control Syst. Mag, 12 (3), pp. 101-107Scherer, C.W., LPV control and full block multipliers (2001) Automatica, 37 (3), pp. 361-375Aouf, N., Bates, D.G., Postlethwaite, I., Boulet, B., Scheduling schemes for an integrated flight and propulsion control system (2002) Contr. Eng. Pract, 10 (1), pp. 685-696Nichols, R.A., Reichert, R.T., Rugh, W.J., Gain scheduling for H-infinity controllers: A flight control example (1993) IEEE Trans. Control Syst. Technol, 1 (2), pp. 69-79De Caigny, J., Camino, J.F., Paijmans, B., Swevers, J., An application of interpolating gain-scheduling control (2007) Proc. 3rd IFAC Symp. Syst., Struct. and Control (SSSC07), , Foz do Iguassu, Brazil, Oct, cdromKhargonekar, P.P., Kaminer, I., Rotea, M.A., Mixed H 2/H∞ control for discrete-time systems via convex optimization (1993) Automatica, 29 (1), pp. 50-77P. L. D. Peres, J. C. Geromel, and S. R. Souza, H 2 output feedback control for discrete-time systems, in Proc. 1994 Amer. Control Conf., Baltimore, MD, USA, 1994, pp. 2429-2433Amato, F., Mattei, M., Pironti, A., Gain scheduled control for discrete-time systems depending on bounded rate parameters (2005) Int. J. Robust Nonlinear Control, 15, pp. 473-494Wu, F., Yang, X.H., Packard, A., Becker, G., Induced L 2-norm control for LPV systems with bounded parameter variation rates (1996) Int. J. Robust Nonlinear Control, 6 (9-10), pp. 983-998de Souza, C.E., Trofino, A., Gain-scheduled H2 controller synthesis for linear parameter varying systems via parameter-dependent Lyapunov functions (2006) Int. J. Robust Nonlinear Control, 16 (5), pp. 243-257Daafouz, J., Bernussou, J., Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties (2001) Syst. Contr. Lett, 43 (5), pp. 355-359Montagner, V.F., Oliveira, R.C.L.F., Leite, V.J.S., Peres, P.L.D., LMI approach for H∞ linear parameter-varying state feedback control (2005) IEE Proc. - Control Theory Appl, 152 (2), pp. 195-201Leite, V.J.S., Peres, P.L.D., Robust control through piecewise Lyapunov functions for discrete time-varying uncertain systems (2004) Int. J. Control, 77 (3), pp. 230-238V. F. Montagner, R. C. L. F. Oliveira, V. J. S. Leite, and P. L. D. Peres, Gain scheduled state feedback control of discrete-time systems with time-varying uncertainties: an LMI approach, in Proc. 44th IEEE Conf. Decision Control - Eur. Control Conf. ECC 2005, Seville, Spain, Dec. 2005, pp. 4305-4310R. C. L. F. Oliveira and P. L. D. Peres, Robust stability analysis and control design for time-varying discrete-time polytopic systems with bounded parameter variation, in Proc. 2008 Amer. Control Conf., Seattle, WA, USA, Jun. 2008, pp. 3094-3099Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory (1994) ser. Stud, 15. , Appl. Math. Philadelphia: SIAMde Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discretetime robust stability condition (1999) Syst. Contr. Lett, 37 (4), pp. 261-265de Oliveira, M.C., Geromel, J.C., Bernussou, J., Extended H2 and H∞ norm characterizations and controller parameterizations for discrete-time systems (2002) Int. J. Control, 75 (9), pp. 666-679Geromel, J.C., Peres, P.L.D., Souza, S.R., Convex analysis of output feedback control problems: Robust stability and performance (1996) IEEE Trans. Autom. Control, 41 (7), pp. 997-100