This paper investigates the finite-time H∞ control problem for discrete-time Markovian jump linear systems with time delay and norm-bounded exogneous disturbance. The stochastic finite-time boundness is achieved by employing an average dwell time approach, which has more design freedom by allowing the stochastic Lyapunov-like function (SLLF) to increase more slowly during the running time of each operation mode. Note that the SLLF increases at every jumping instant rather than at every sampling time instant. Sufficient conditions for the solvability of the controller, which are dependent or independent on the time delay, are given in terms of linear matrix inequalities. Numerical examples are given to verify the efficiency of the proposed method.
AmatoFAmbrosinoRAriolaM. (2009) Finite-time stability of linear time-varying systems with jumps. Automatica45(5): 1354–1358.
2.
AmatoFAmbrosinoRCosentinoC. (2010a) Input–output finite time stabilization of linear systems. Automatica46(9): 1558–1562.
3.
AmatoFAriolaM (2005) Finite-time control of discrete-time linear systems. IEEE Transactions on Automatic Control50(5): 724–729.
4.
AmatoFAriolaMCosentinoC (2010b) Finite-time control of discrete-time linear systems: analysis and design conditions. Automatica46(5): 919–924.
5.
AmatoFAmbrosinoRCosentinoC. (2011) Finite-time stabilization of impulsive dynamical linear systems. Nonlinear Analysis: Hybrid Systems5(1): 89–101.
6.
AmatoFAriolaMDoratoP (2001) Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica37(9): 1459–1463.
7.
BolzernPColaneriPNicolaoG (2010) Markov jump linear systems with switching transition rates: mean square stability with dwell-time. Automatica46(6): 1081–1088.
8.
ChengTCEGaoCYShengHC (2011) Production and inventory rationing in a Make-to-Stock system with a failure-prone machine and lost sales. IEEE Transactions on Automatic Control56(6): 1176–1180.
9.
CostaOLVFilhoEOABoukasEK. (1999) Constrained quadratic state feedback control of discrete-time Markovian jump linear systems. Automatica35(4): 617–626.
10.
HeSPLiuF (2010a) Stochastic finite-time stabilization for uncertain jump systems via state feedback. Journal of Dynamic Systems Measurement and Control Transactions of the ASME132(3): 1–4.
11.
HeSPLiuF (2010b) Observer-based finite-time control of time-delayed jump systems. Applied Mathematics and Computation217(6): 2327–2338.
12.
HeSPLiuF (2010c) Robust finite-time stabilization of uncertain fuzzy jump systems. International Journal of Innovative Computing Information and Control6(9): 3853–3862.
13.
HeSPLiuF (2011) Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities. Applied Mathematical Modeling35(6): 2631–2638.
14.
HeSPLiuF (2012a) Finite-time fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback. IEEE Transactions on Fuzzy Systems20(4): 605–614.
15.
HeSPLiuF (2012b) On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval. Transactions of the Institute of Measurement and Control34(7): 841–849.
16.
HeSPLiuF (2013) Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters. Neurocomputing103(1): 87–92.
17.
HouLLZongGDWuYQ (2012) Finite-time control for switched delay systems via dynamic output feedback. International Journal of Innovative Computing, Information and Control8(7): 4901–4913.
18.
LeeJDullerudG (2006) Uniform stabilization of discrete-time switched and Markovian jump linear systems. Automatica42(2): 205–218.
19.
LianJShiPFengZ (2013) Passivity and passification for a class of uncertain switched stochastic time-delay systems. IEEE Transactions on Cybernetics43(1): 3–13.
20.
LinJXFeiSMShenJ (2011) Delay-dependent H∞ filtering for discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities. Signal Processing91(2): 277–289.
21.
LiuJLGuZHuSL (2011) H∞ filtering for Markovian jump systems with time-varying delays. International Journal of Innovative Computing, Information and Control7(3): 1299–1310.
22.
LuanXLLiuFShiP (2010a) Neural-network-based finite-time H∞ control for extended Markov jump nonlinear systems. International Journal of Adaptive Control and Signal Processing24(7): 554–567.
23.
LuanXLLiuFShiP (2010b) Robust finite-time H∞ control for nonlinear jump systems via neural networks. Circuits Systems and Signal Processing29(3): 481–498.
24.
LuanXLLiuFShiP (2011a) Observer-based finite-time stabilization for extended Markov jump systems. Asian Journal of Control13(6): 925–935.
25.
LuanXLLiuFShiP (2011b) Robust finite-time control for a class of extended stochastic switching systems. International Journal of Systems Science42(7): 1197–1205.
26.
MoulayEDambrineMYeganefarN. (2008) Finite-time stability and stabilization of time-delay systems. Systems & Control Letters57(7): 561–566.
27.
ShiPXiaYLiuG. (2006) On designing of sliding mode control for stochastic jump systems. IEEE Transactions on Automatic Control51(1): 97–103.
28.
SongHYYuLZhangD. (2012) Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback. Communications in Nonlinear Science and Numerical Simulation17(12): 4802–4814.
29.
WangDShiPWangJL. (2012) Delay-dependent exponential H∞ filtering for discrete-time switched delay systems. International Journal of Robust and Nonlinear Control22(13): 1522–1536.
30.
WangDWangJLWangW (2013) H∞ controller design of networked control systems with Markov packet dropouts. IEEE Transactions on Systems, Man, and Cybernetics: Systems43(3): 689–697.
31.
WangGLZhangQLSreeramV (2010) Partially mode-dependent H∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities. Signal Processing90(2): 548–556.
32.
WeissLInfanteE (1967) Finite time stability under perturbing forces and on product spaces. IEEE Transactions on Automatic Control12(1): 54–59.
33.
XiangZRQiaoCHMahmoudMS (2012a) Finite-time analysis and H∞ control for switched stochastic systems. Journal of the Franklin Institute349(3): 915–927.
34.
XiangZRSunYNMahmoudMS (2012b) Robust finite-time H∞ control for a class of uncertain switched neutral systems. Communications in Nonlinear Science and Numerical Simulation17(4): 1766–1778.
35.
YangDDCaiKY (2010) Finite-time quantized guaranteed cost fuzzy control for continuous-time nonlinear systems. Expert Systems with Applications37(10): 6963–6967.
36.
ZhangLX (2009) H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems. Automatica45(11): 2570–2576.
37.
ZhangLXBoukasEK (2009a) Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica45(2): 463–468.
38.
ZhangLXBoukasEK (2009b) Mode-dependent H∞ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Automatica45(6): 1462–1467.
39.
ZhangXFFengGSunYH (2012) Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems. Automatica48(3): 499–504.
40.
ZhangYHeYWuM. (2011) Mode-dependent H∞ filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Automatica47(1): 79–84.
41.
ZhaoXZengQ (2010) Delay-dependent H∞ performance analysis for Markovian jump systems with mode-dependent time varying delays and partially known transition rates. International Journal of Control, Automation & Systems8(2): 482–489.
