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Periodically time-varying memory static output feedback control design for discrete-time LTI systems. (English) Zbl 1309.93066

Summary: This paper addresses the problem of Static Output Feedback (SOF) stabilization for discrete-time LTI systems. We approach this problem using the recently developed Periodically Time-Varying Memory State-Feedback Controller (PTVMSFC) design scheme. A Bilinear Matrix Inequality (BMI) condition which uses a pre-designed PTVMSFC is developed to design the Periodically Time-Varying Memory SOF Controller (PTVMSOFC). The BMI condition can be solved by using BMI solvers. Alternatively, we can apply two-steps and iterative linear matrix inequality algorithms that alternate between the PTVMSFC and PTVMSOFC designs. Finally, an example is given to illustrate the proposed methods.

MSC:

93B52 Feedback control
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
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[2] Agulhari, C. M.; Oliveira, R. C.L. F.; Peres, P. L.D., LMI relaxations for reduced-order robust \(H_\infty\) control of continuous-time uncertain linear systems, IEEE Transactions on Automatic Control, 57, 6, 1532-1537 (2012) · Zbl 1369.93471
[4] Bara, G. I.; Boutayeb, M., Static output feedback stabilization with \(H_\infty\) performance for linear discrete-time systems, IEEE Transactions on Automatic Control, 50, 2, 250-254 (2005) · Zbl 1365.93434
[5] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory (1994), SIAM: SIAM Philadelphia, PA
[7] Cao, Y.; Lam, J.; Sun, Y., Static output feedback stabilization: an ILMI approach, Automatica, 34, 12, 1641-1645 (1998) · Zbl 0937.93039
[8] Crusius, C. A.R.; Trofino, A., Sufficient LMI conditions for output feedback control problems, IEEE Transactions on Automatic Control, 44, 5, 1053-1057 (1999) · Zbl 0956.93028
[9] de Oliveira, M. C.; Bernussou, J.; Geromel, J. C., A new discrete-time robust stability condition, Systems & Control Letters, 37, 4, 261-265 (1999) · Zbl 0948.93058
[10] de Oliveira, M. C.; Geromel, J. C.; Bernussou, J., Extended \(H_2\) and \(H_\infty\) norm characterizations and controller parameterizations for discrete-time systems, International Journal of Control, 75, 9, 666-679 (2002) · Zbl 1029.93020
[11] Dong, J.; Yang, G.-H., Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties, IEEE Transactions on Automatic Control, 52, 10, 1930-1936 (2007) · Zbl 1366.93460
[12] Dong, J.; Yang, G.-H., Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties, Automatica, 49, 6, 1821-1829 (2013) · Zbl 1360.93244
[14] Ebihara, Y.; Peaucelle, D.; Arzelier, D., Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems, Automatica, 47, 1, 14-25 (2011) · Zbl 1209.93092
[15] El Ghaoui, L.; Oustry, F.; AitRami, M., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control, 42, 8, 1171-1176 (1997) · Zbl 0887.93017
[16] Fu, M.; Luo, Z., Computational complexity of a problem arising in fixed order output feedback design, Systems & Control Letters, 30, 5, 209-215 (1997) · Zbl 0901.93023
[17] Fujimori, A., Optimization of static output feedback using substitutive LMI formulation, IEEE Transactions on Automatic Control, 49, 6, 995-999 (2004) · Zbl 1365.93396
[18] Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M., LMI control toolbox for use with MATLAB, user’s guide (1995), The Math Works Inc.: The Math Works Inc. Natick, MA, USA
[19] Garcia, G.; Pardin, B.; Zeng, F., Stabilization of discrete time linear systems by static output feedback, IEEE Transactions on Automatic Control, 46, 12, 1954-1958 (2001) · Zbl 1009.93066
[21] He, Y.; Wang, Q, -G., An improved ILMI method for static output feedback control with applicatoin to multivariable PID control, IEEE Transactions on Automatic Control, 51, 10, 1678-1683 (2006) · Zbl 1366.93218
[23] Iwasaki, T.; Skelton, R. E., All controllers for the general \(H_\infty\) control problem: LMI existence conditions and state space formulas, Automatica, 30, 8, 1307-1317 (1994) · Zbl 0806.93017
[24] Kanev, S.; Scherer, C.; Verhaegen, M.; de Schutter, B., Robust output-feedback controller design via local BMI optimization, Automatica, 40, 7, 1115-1127 (2004) · Zbl 1051.93042
[26] Kučera, V.; de Souza, C. E., A necessary and sufficient condition for output feedback stabilizability, Automatica, 31, 9, 1357-1359 (1995) · Zbl 0831.93056
[28] Lee, K. H.; Lee, J. H.; Kwon, W. H., Sufficient LMI conditions for \(H_\infty\) output feedback stabilization of linear discrete-time systems, IEEE Transactions on Automatic Control, 51, 4, 675-680 (2006) · Zbl 1366.93505
[30] Mehdi, D.; Boukas, E. K.; Bachelier, O., Static output feedback design for uncertain linear discrete time systems, IMA Journal of Mathematical Control and Information, 21, 1, 1-13 (2004) · Zbl 1049.93069
[31] Oliveira, R. C.L. F.; de Oliveira, M. C.; Peres, P. L.D., Convergent LMI relaxations for robust analysis of uncertain linear systems using lifted polynomial parameter-dependent Lyapunov functions, Systems & Control Letters, 57, 8, 680-689 (2008) · Zbl 1140.93453
[32] 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, IEEE Transactions on Automatic Control, 52, 7, 1334-1340 (2007) · Zbl 1366.93472
[33] Orsi, R.; Helmke, U.; Moore, J. B., A Newton-like method for solving rank constrained linear matrix inequalities, Automatica, 42, 11, 1875-1882 (2006) · Zbl 1222.90032
[35] Peaucelle, D.; Arzelier, D., Ellipsoidal sets for resilient and robust static output-feedback, IEEE Transactions on Automatic Control, 50, 6, 899-904 (2005) · Zbl 1365.93121
[36] Peaucelle, D.; Arzelier, D.; Bachelier, O.; Bernussou, J., A new robust \(D\)-stability condition for real convex polytopic uncertainty, Systems & Control Letters, 40, 1, 21-30 (2000) · Zbl 0977.93067
[37] Prempain, E.; Postlethwaite, I., Static output feedback stabilization with \(H_\infty\) performance for a class of plants, Systems & Control Letters, 43, 3, 159-166 (2001) · Zbl 0974.93054
[38] Rosinová, D.; Veselý, V.; Kučera, V., A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems, Kybernetika, 39, 4, 447-459 (2003) · Zbl 1249.93150
[39] Scherer, C.; Gahinet, P.; Chilali, M., Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, 42, 7, 896-911 (1997) · Zbl 0883.93024
[40] Shu, Z.; Lam, J.; Xiong, J., Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach, Automatica, 46, 4, 687-694 (2010) · Zbl 1193.93149
[41] Skelton, R. E.; Iwasaki, T.; Grioriadis, K., A unified algebraic approach to linear control design (1998), Taylor & Francis: Taylor & Francis London
[42] Strum, J. F., Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods · Zbl 0973.90526
[45] Trégouët, J. -F.; Peaucelle, D.; Arzelier, D.; Ebihara, Y., Periodic memory state-feedback controller: new formulation, analysis, and design results, IEEE Transactions on Automatic Control, 58, 8, 1986-2000 (2013) · Zbl 1369.93353
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