Parameter-dependent finite-time observer design for time-varying polytopic uncertain switched systems. (English) Zbl 1395.93345
Summary: Mathematical models are an approximate of physical systems and design procedures are only complete when modeling errors have been quantified. Uncertainties are incorporated in design procedure to compensate such discrepancies and to add robustness. This paper investigates the design problem of parameter-dependent switched observers for polytopic uncertain switched systems. State-space model is considered subject to time-varying uncertainties, and designated observer gains ensuring stability of overall system are also parameter-dependent. Synthesis procedure is demonstrated by employing \(\mathcal H_\infty\) performance criteria which has become a standard for robust system design against external disturbances. This investigation is carried out in the framework of finite-time stability (FTS) and finite-time boundedness (FTB) which is the focus of researchers recently because of its apparent practical significance, especially after the emergent utilization of linear matrix inequalities.
MSC:
| 93C55 | Discrete-time control/observation systems |
| 93E11 | Filtering in stochastic control theory |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93D15 | Stabilization of systems by feedback |
| 93C41 | Control/observation systems with incomplete information |
| 93B50 | Synthesis problems |
| 93B36 | \(H^\infty\)-control |
Keywords:
finite-time observer design; uncertain switched systems; time-varying polytopic systems; \(\mathcal H_\infty\) performanceReferences:
| [1] | Lin, H.; Antsaklis, P. J., Stability and stabilizability of switched linear systems: a survey of recent results, IEEE Trans. Automat. Control, 54, 2, 308-322, (2009) · Zbl 1367.93440 |
| [2] | Mahmoud, M. S., switched time-delay systems: stability and control, (2010), Springer USA · Zbl 1229.93001 |
| [3] | Zhang, L.; Shi, P.; Boukas, E. K.; Wang, C., Robust l2-l∞ filtering for switched linear discrete time-delay systems with polytopic uncertainties, IET Control Theory Appl., 1, 3, 722-730, (2007) |
| [4] | Daafouz, J.; Millerioux, G.; Iung, C., A poly-quadratic stability based approach for linear switched systems, Int. J. Control, 75, 16-17, 1302-1310, (2002) · Zbl 1017.93025 |
| [5] | Zhang, L.; Shi, P.; Boukas, E.-K.; Wang, C., H_{∞}model reduction for uncertain switched linear discrete-time systems, Automatica, 44, 11, 2944-2949, (2008) · Zbl 1152.93321 |
| [6] | Daafouz, J.; Riedinger, P.; Iung, C., Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach, IEEE Trans. Automat. Control, 47, 11, 1883-1887, (2002) · Zbl 1364.93559 |
| [7] | Xiang, W.; Xiao, J., H_{∞}controller design for a class of switched linear discrete-time system with polytopic uncertainties, Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng., (2012) |
| [8] | Zhang, L.; Wang, C.; Chen, L., Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties, IEEE Trans. Ind. Electron., 56, 9, 3684-3692, (2009) |
| [9] | Amato, F.; Ariola, M.; Carbone, M.; Cosentino, C., Finite-time control of linear systems: a survey, (Menini, L.; Zaccarian, L.; Abdallah, C. T., Current Trends in Nonlinear Systems and Control, (2006), Birkhäuser Boston), 195-213 |
| [10] | H. Du , X. Lin, S. Li, Finite-time stability and stabilization of switched linear systems, in: 48th IEEE Conference on Decision and Control, 2009, Institute of Electrical and Electronics Engineers Inc., Shanghai, China, 2009. |
| [11] | Iqbal, M. N.; Xiao, J.; Xiang, W., finite time H_{∞}filtering for uncertain discrete-time switching systems, Trans. Inst. Meas. Control, 35, 6, 851-862, (2013) |
| [12] | Xiang, W.; Xiao, J.; Xiao, C., On finite-time stability and stabilization for switched discrete linear systems, Control Intell. Syst., 39, 2, 122-128, (2011) · Zbl 1282.93212 |
| [13] | Xiang, W.; Xiao, J., Finite-time stability and stabilisation for switched linear systems, Int. J. Syst. Sci., 44, 2, 384-400, (2013) · Zbl 1307.93366 |
| [14] | Xiang, W.; Xiao, J., H_{∞}finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance, J. Frankl. Inst., 348, 2, 331-352, (2011) · Zbl 1214.93043 |
| [15] | Hao Liu, Y. S., H_{∞}finite-time control for switched linear systems with time-varying delay, Intell. Control Autom., 2, 3, 203-213, (2011) |
| [16] | Alessandri, A.; Baglietto, M.; Battistelli, G., Luenberger observers for switching discrete-time linear systems, Int. J. Control, 80, 12, 1931-1943, (2007) · Zbl 1152.93371 |
| [17] | Zames, G., Feedback and optimal sensitivity - model reference transformations, multiplicative seminorms, and approximate inverses, IEEE Trans. Autom. Control, AC-26, 2, 301-320, (1981) · Zbl 0474.93025 |
| [18] | Elsayed, A.; Grimble, M. J., new approach to the H_{∞}design of optimal digital linear filters, IMA J. Math. Control Inf., 6, 2, 233-251, (1989) · Zbl 0678.93063 |
| [19] | Xiang, W.; Xiao, J.; Iqbal, M. N., Robust observer design for nonlinear uncertain switched systems under asynchronous switching, Nonlinear Anal.: Hybrid Syst., 6, 1, 754-773, (2012) · Zbl 1235.93053 |
| [20] | Mahmoud, M. S.; Shi, P., asynchronous H_{∞}filtering of discrete-time switched systems, Signal Process., 92, 10, 2356-2364, (2012) |
| [21] | Wang, D.; Shi, P.; Wang, J.; Wang, W., delay-dependent exponential H_{∞}filtering for discrete-time switched delay systems, Int. J. Robust Nonlinear Control, 22, 13, 1522-1536, (2012) · Zbl 1287.93096 |
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