Switching Markov jump linear system (SMJLS), a special hybrid system, has attracted a lot of studies
recently. SMJLS is governed by stochastic and deterministic commutations. This paper focuses on the switching
strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results
and investigate new aspects of such systems. Several sufficient conditions for finite-time stability of discrete-time
SMJLS are provided, and the numerical problems in these sufficient conditions are solved by solving linear matrix
inequalities (LMIs). Finally, numerical examples are given to show the feasibility and effectiveness of the results.
JIN Yunyun, SONG Yang, LIU Yongzhuang, HOU Weiyan
. Finite-Time Stability and Stabilization of Discrete-Time Switching Markov Jump Linear System[J]. Journal of Shanghai Jiaotong University(Science), 2020
, 25(5)
: 674
-680
.
DOI: 10.1007/s12204-020-2205-0
[1] FENGW, ZHANG J F. Mean square stabilization control of switched systems with stochastic disturbances [C]//43rd IEEE Conference on Decision and Control(CDC). Nassau, Bahamas: IEEE, 2004: 3714-3719.
[2] BRANICKY M S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems [J]. IEEE Transactions on Automatic Control, 1998,43(4): 475-482.
[3] CHENG D Z, GUO L, LIN Y D, et al. Stabilization of switched linear systems [J]. IEEE Transactions on Automatic Control, 2005, 50(5): 661-666.
[4] HESPANHA J P, MORSE A S. Stability of switched systems with average dwell-time [C]//Proceedings of the 38th IEEE Conference on Decision and Control.Phoenix. AZ, USA: IEEE, 2002: 2655-2660.
[5] LIBERZON D, HESPANHA J P, MORSE A S. Stability of switched systems: a Lie-algebraic condition [J].Systems & Control Letters, 1999, 37(3): 117-122.
[6] SHORTEN R N, NARENDRA K S. On the stability and existence of common Lyapunov functions for stable linear switching systems [C]//Proceedings of the 37th IEEE Conference on Decision and Control.Tampa, FL, USA: IEEE, 1998: 3723-3724.
[7] DAAFOUZ J, RIEDINGER P, IUNG C. Stability analysis and control synthesis for switched systems:a switched Lyapunov function approach [J]. IEEE Transactions on Automatic Control, 2002, 47(11):1883-1887.
[8] EL-FARRA N H, CHRISTOFIDES P D. Switching and feedback laws for control of constrained switched nonlinear systems [M]//Hybrid systems: Computation and control. Berlin, Heidelberg: Springer, 2002, 164-178.
[9] FERRON K E. Quadratic stabilizability of switched systems via state and output feedback [R]. Cambridge,USA: MIT Center for Intelligent Control Systems,1996: 1-13.
[10] GIUA A, SEATZU C, VAN DER MEE C. Optimal control of switched autonomous linear systems[C]//Proceedings of the 40th IEEE Conference on Decision and Control. Orlando, FL, USA: IEEE, 2001:2472-2477.
[11] SKAFIDAS E, EVANS R J, MAREELS I M Y, et al. Optimal controller switching for stochastic systems[M]//Hyrbrid system V. Berlin, Heidelberg: Springer,1999: 341-355.
[12] ZHANG L X, BOUKAS E K, BARON L. Fault detection for discrete-time Markov jump linear systems with partially known transition probabilities [C]//47th IEEE Conference on Decision and Control. Cancun,Mexico: IEEE, 2008: 1054-1059.
[13] BOLZERN P, COLANERI P, DE NICOLAO G. Almost sure stability of continuous-time Markov jump linear systems: A randomized approach [J]. IFAC Proceedings Volumes, 2005, 38(1): 7-12.
[14] HUANG J, SHI Y, ZHANG X. Active fault tolerant control systems by the semi-Markov model approach [J]. International Journal of Adaptive Control and Signal Processing, 2014, 28(9): 833-847.
[15] BOLZERN P, COLANERI P, DE NICOLAO G.Stochastic stability of positive Markov jump linear systems[J]. Automatica, 2014, 50(4): 1181-1187.
[16] XIAO N, XIE L H, FU M Y. Stabilization of Markov jump linear systems using quantized state feedback [J].Automatica, 2010, 46(10): 1696-1702.
[17] FANG Y G, LOPARO K A. Stabilization of continuous-time jump linear systems [J]. IEEE Transactions on Automatic Control, 2002, 47(10): 1590-1603.
[18] SONG Y, DONG H, YANG T C, et al. Almost sure stability of discrete-time Markov jump linear systems[J]. IET Control Theory & Applications, 2014, 8(11):901-906.
[19] DOCOSTAOL V, MARQUESR P, FRAGOSOMD.Discrete-time Markov jump linear systems [M]. London:Springer, 2005.
[20] DORATO P. Short time stability in linear time-varying systems [C]//Proceedings of the IRE International Convention Record. New York: Polytechnic Institute of Brooklyn, 1961: 83-87.
[21] WEISS L, INFANTE E F. Finite time stability under perturbing forces and on product spaces [J]. IEEE Transactions on Automatic Control, 1967, 12(1): 54-59.
[22] DULLERUD G E, LALL S G. Analysis and synthesis tools for time-varying systems [C]//Proceedings of the 36th IEEE Conference on Decision and Control. San Diego, CA, USA: IEEE, 1997: 4543-4548.
