Artículos de revistas
Delay-dependent Robust H∞ Filter Design For State-delayed Discrete-time Linear Systems Via Homogeneous Polynomial Matrices
Registro en:
Iet Control Theory And Applications. , v. 7, n. 1, p. 125 - 135, 2013.
17518644
10.1049/iet-cta.2012.0682
2-s2.0-84877754688
Autor
Lacerda M.J.
Leite V.J.S.
Oliveira R.C.L.F.
Peres P.L.D.
Institución
Resumen
This study presents new robust linear matrix inequality (LMI) conditions for robust H∞ full-order filter design of discrete-time linear systems affected by time-invariant uncertainty and a time-varying state delay. Thanks to the use of a larger number of slack variables, the proposed robust LMI conditions contain and generalise other results from the literature. LMI relaxations based on homogeneous polynomial matrices of arbitrary degree are used to determine the state-space realisation of the full-order filter, that can also be implemented with delayed state terms whenever the time-delay is available in real time. As another contribution, an iterative LMI-based procedure involving the decision variables is proposed to improve the H∞ filter performance. Numerical experiments illustrate the better performance of the proposed filter when compared to other approaches available in the literature. © 2013 The Institution of Engineering and Technology. 7 1 125 135 Niculescu, S.-I., Delay effects on stability: A robust control approach (2001) Lecture Notes Series in Control and Information Sciences, 269. , Springer-Verlag, London Richard, J.-P., Time-delay systems: An overview of some recent advances and open problems (2003) Automatica, 39 (10), pp. 1667-1694 Leite, V.J.S., Peres, P.L.D., Castelan, E.B., Tarbouriech, S., On the robust stability of neutral systems with time-varying delays (2005) Proc. 16th IFAC World Congress, , Prague, Czech Republic July in CD-rom Peet, M.M., Papachristodoulou, A., Lall, S., Positive forms and stability of linear time-delay systems (2009) SIAM J. Control Optim., 47 (6), pp. 3237-3258 Coutinho, D.F., De Souza, C.E., Delay-dependent robust stability and L 2-gain analysis of a class of nonlinear time-delay systems (2008) Automatica, 44 (8), pp. 2006-2018 Huang, H., Feng, G., Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay (2010) IET Control Theory Appl., 4 (10), pp. 2152-2159 Chen, J.-D., Robust control for uncertain neutral systems with time-delays in state and control input via LMI and GAs (2004) Appl. Math. Comput., 157 (2), pp. 535-548 Fridman, E., Shaked, U., Delay dependent H1 control of uncertain discrete delay system (2005) Eur. J. Control, 11 (1), pp. 29-37 Wu, Z., Zhou, W., Delay-dependent robust H1 control for uncertain singular time-delay systems (2007) IET Control Theory Appl., 1 (5), pp. 1234-1241 Leite, V.J.S., Tarbouriech, S., Peres, P.L.D., Robust H1 state feedback control of discrete-time systems with state delay: An LMI approach (2009) IMA J. Math. Control Inf., 26 (3), pp. 357-373 Miranda, M.F., Leite, V.J.S., Caldeira, A.F., Robust stabilization of polytopic discrete-time systems with time-varying delay in the states (2010) Proc. 49th IEEE Conf. on Decision and Control, pp. 152-157. , Atlanta, GA, USA, December Nguang, S.K., Shi, P., Delay-dependent H1 filtering for uncertain time delay nonlinear systems: An LMI approach (2007) IET Control Theory Appl., 1 (1), pp. 133-140 Gao, H., Meng, X., Chen, T., A parameter-dependent approach to robust H1 filtering for time-delay systems (2008) IEEE Trans. Autom. Control, 53 (10), pp. 2420-2425 Yang, R., Gao, H., Shi, P., Delay-dependent L 2-L1 filter design for stochastic time-delay systems discrete time-delay systems (2011) IET Control Theory Appl., 5 (1), pp. 1-8 Larsen, T.D., Andersen, N.A., Ravn, O., Poulsen, N.K., Incorporation of time delayed measurements in a discrete-time Kalman filter (1998) Proc. 37th IEEE Conf. on Decision and Control, pp. 3972-3977. , Tampa, FL, USA, December Palhares, R.M., De Souza, C.E., Peres, P.L.D., Robust H1 filtering for uncertain discrete-time state-delayed systems (2001) IEEE Trans. Signal Process., 49 (8), pp. 1096-1703 Gao, H., Wang, C., A delay-dependent approach to robust H1 filtering for uncertain discrete-time state-delayed systems (2004) IEEE Trans. Signal Process., 52 (6), pp. 1631-1640 Souza, F.O., Palhares, R.M., Barbosa, K.A., New improved delay-dependent H1 filter design for uncertain neutral systems (2008) IET Control Theory Appl., 2 (12), pp. 1033-1043 Xu, S., Robust H1 filtering for a class of discrete-time uncertain nonlinear systems with state delay (2002) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 49 (12), pp. 1853-1859 Zhang, L., Shi, P., Boukas, E.-K., Wang, C., Robust L 2-L1 filtering for switched linear discrete time-delay systems with polytopic uncertainties (2007) IET Control Theory Appl., 1 (3), pp. 722-730 Qiu, J., Feng, G., Yang, J., New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay (2008) IET Control Theory Appl., 2 (9), pp. 795-806 Du, D., H1 filter for discrete-time switched systems with time-varying delays (2010) Nonlinear Anal. Hybrid Syst., 4 (4), pp. 782-790 Zhang, H., Shi, Y., Saadat Mehr, A., Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data (2010) IET Control Theory Appl., 4 (12), pp. 2921-2936 Qiu, J., Feng, G., Yang, J., A new design of delay-dependent robustH1 filtering for discrete-time T-S fuzzy systems with time-varying delay (2009) IEEE Trans. Autom. Control, 17 (5), pp. 1044-1058 Kim, J.H., Reduced-order delay-dependent H1 filtering for uncertain discrete-time singular systems with time-varying delay (2011) Automatica, 47 (12), pp. 2801-2804 Geromel, J.C., Bernussou, J., Garcia, G., De Oliveira, M.C., H 2 and H1 robust filtering for discrete-time linear systems (2000) SIAM J. Control Optim., 38 (5), pp. 1353-1368 Palhares, R.M., Peres, P.L.D., Robust filtering with guaranteed energy-to-peak performance - An LMI approach (2000) Automatica, 36 (6), pp. 851-858 Palhares, R.M., Peres, P.L.D., LMI approach to the mixed H2/H1 filtering design for discrete-time uncertain systems (2001) IEEE Trans. Aerosp. Electron. Syst., 37 (1), pp. 292-296 Geromel, J.C., De Oliveira, M.C., Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions (2002) SIAM J. Control Optim., 41 (3), pp. 700-711 Duan, Z.S., Zhang, J.X., Zhang, C.S., Mosca, E., Robust H2 and H1 filtering for uncertain linear systems (2006) Automatica, 42 (11), pp. 1919-1926 Gao, H., Meng, X., Chen, T., A new design of robust H2 filters for uncertain systems (2008) Syst. Control Lett., 57 (7), pp. 585-593 Lacerda, M.J., Oliveira, R.C.L.F., Peres, P.L.D., Robust H2 and H1 filter design for uncertain linear systems via LMIs and polynomial matrices (2011) Signal Process., 91 (5), pp. 1115-1122 De Souza, C.E., Barbosa, K.A., Trofino, A., Robust H1 filtering for discrete-time linear systems with uncertain time-varying parameters (2006) IEEE Trans. Signal Process., 54 (6), pp. 2110-2118 Lacerda, M.J., Oliveira, R.C.L.F., Peres, P.L.D., H1 parameter-dependent filter design for arbitrarily time-varying LPV systems Proc. 18th IFAC World Congress, pp. 7927-7932. , Milano, Italy, September 2011 Gao, H., Meng, X., Chen, T., H1 filter design for discrete delay systems: A new parameter-dependent approach (2009) Int. J. Control, 82 (6), pp. 993-1005 Li, X., Li, Z., Gao, H., Further results on H1 filtering for discrete-time systems with state delay (2011) Int. J. Robust Nonlinear Control, 21 (3), pp. 248-270 Lacerda, M.J., Leite, V.J.S., Oliveira, R.C.L.F., Peres, P.L.D., Robust H1 filter design for polytopic discrete-time delay systems via LMIs and polynomial matrices (2011) Proc. 50th IEEE Conf. on Decision and Control - European Control Conf. (ECC 2011), pp. 8225-8230. , Orlando, FL, USA, December Zhu, X.L., Yang, G.H., Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay (2008) Proc. 2008 American Control Conf., pp. 1644-1649. , Seattle, WA, USA June De Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems (2001) Perspectives in Robust Control', Lecture Notes Series in Control and Information Science, 268, pp. 241-257. , Reza Moheimani, S.O. (Ed.) Springer-Verlag, New York Oliveira, R.C.L.F., Peres, P.L.D., Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations (2007) IEEE Trans. Autom. Control, 52 (7), pp. 1334-1340 Bliman, P.-A., Oliveira, R.C.L.F., Montagner, V.F., Peres, P.L.D., Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex (2006) Proc. 45th IEEE Conf. on Decision and Control, pp. 1486-1491. , San Diego, CA, USA, December Löfberg, J., YALMIP: A toolbox for modeling and optimization in MATLAB (2004) Proc. 2004 IEEE Int. Symp. on Computer Aided Control Systems Design, pp. 284-289. , http://control.ee.ethz.ch/joloef/yalmip.php, Taipei, Taiwan, September Sturm, J.F., Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones (1999) Optim. Methods Softw., 11 (1-4), pp. 625-653. , http://sedumi.mcmaster.ca/