The paper is concerned with finite-time dissipativity analysis and design for stochastic Markovian jump systems with generally uncertain transition rates and time-varying delay. By constructing a more appropriate Lyapunov–Krasovskii functional, sufficient conditions for finite-time dissipativity of the underlying system are first proposed. Then, a state feedback controller is designed such that the closed-loop Markovian jump system is finite-time dissipative. These sufficient criteria are derived in the form of linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the validity of the main results.
CuiWXFangJAShenYL. (2013) Dissipativity analysis of singular systems with Markovian jump parameters and mode-dependent mixed time-delays. Neurocomputing110: 121–127.
2.
DingYCZhuHZhongSM. (2013) H∞ filtering for stochastic systems with Markovian switching and partly unknown transition probabilities. Circuits, Systems, and Signal Processing32(2): 559–583.
3.
DongXZ (2007) Robust strictly dissipative control for discrete singular systems. IET Control Theory and Applications1(4): 1060–1067.
4.
DoratoP (1961) Short time stability in linear time-varying systems. Proceedings of the IRE International Convention Record, New York4: 83–87
5.
FengZLamJ (2011) Stability and dissipativity analysis of distributed delay cellular neural networks. IEEE Transactions on Neural Networks22(6): 976–981.
6.
FengZGLamJGaoHJ (2011) α-dissipativity analysis of singular time-delay systems. Automatica47(11): 2548–2552.
7.
GeXHHanQL (2014) Distributed fault detection over sensor networks with Markovian switching topologies. International Journal of General Systems43(3–4): 305–318.
8.
GuoYFWangZJ (2013) Stability of Markovian jump systems with generally uncertain transition rates. Journal of the Franklin Institute350(9): 2826–2836.
9.
HillDJMoylanPJ (1976) The stability of nonlinear dissipative systems. IEEE Transactions on Automatic Control21(5): 708–711.
10.
HillDJMoylanPJ (1980) Dissipative dynamical systems: Basic input–output and state properties. Journal of the Franklin Institute309(5): 327–357.
11.
KaoYGXieJWangCH (2014a) Stabilisation of singular Markovian jump systems with generally uncertain transition rates. IEEE Transactions on Automatic Control59(9): 2604–2610.
12.
KaoYGXieJWangCH (2014b) Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates. Applied Mathematics and Computation245: 243–254.
13.
KaoYGXieJWangCH. (2015) A sliding mode approach to H∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems. Automatica52: 218–226.
14.
MahmoudMSSaifAWA (2013) Dissipativity analysis and design for uncertain Markovian jump systems with time-varying delays. Applied Mathematics and Computation219(18): 9681–9695.
15.
MaYHYanHJ (2013) Delay-dependent non-fragile robust dissipative filtering for uncertain nonlinear stochastic singular time-delay systems with Markovian jump parameters. Advances in Difference Equations2013: 135–154.
16.
Meisami-AzadMMohamnadpourJGrigoriadisKM (2009) Dissipative analysis and control of state-space symmetric systems. Automatica45(6): 58–73.
17.
QiWHGaoXW (2015) Finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity. International Journal of Systems Science. Epub online ahead of print 1 April 2015. DOI:10.1080/00207721.2015.1025891.
18.
QiWHGaoXWLiYX (2015) Robust H-infinity control for stochastic Markovian switching systems under partly known transition probabilities and actuator saturation via anti-windup design. Circuits, Systems, and Signal Processing34(7): 2141–2165.
19.
SenthilkumarTBalasubramaniamP (2011) Delay-dependent robust stabilization and H∞ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays. Journal of Optimization Theory and Applications151(1): 100–120.
20.
ShaoHY (2008) Delay-range-dependent robust H∞ filtering for uncertain stochastic systems with mode dependent time delays and Markovian jump parameters. Journal of Mathematical Analysis and Applications342(2): 1084–1095.
21.
ShenHParkJHZhangLX. (2014a) Robust extended dissipative control for sampled-data Markov jump systems. International Journal of Control87(8): 1549–1564.
22.
ShenHWuZGParkJH (2014b) Reliable mixed passive and H∞ filtering for semi-Markov jump systems with randomly occurring uncertainties and sensor failures. International Journal of Robust and Nonlinear Control. Epub online ahead of print 15 October 2014. DOI: 10.1002/rnc.3255.
23.
ShenHWuZGParkJH (2014c) Finite-time energy-to-peak filtering for Markov jump repeated scalar non-linear systems with packet dropouts. IET Control Theory and Applications8(16): 1617–1624.
24.
ShenLJBuscherU (2012) Solving the serial batching problem in job shop manufacturing systems. European Journal of Operational Research221(1): 14–26.
25.
SongJHeSP (2015) Finite-time robust passive control for a class of uncertain Lipschitz nonlinear systems with time-delays. Neurocomputing159: 275–281.
26.
SongYXieJXFeiMR. (2013) Mean square exponential stabilization of networked control systems with Markovian packet dropouts. Transactions of the Institute of Measurement and Control35(1): 75–82.
27.
WangGL (2011) Partially mode-dependent design of H-infinity filter for stochastic Markovian jump systems with mode-dependent time delays. Journal of Mathematical Analysis and Applications383(2): 573–584.
28.
WangGL (2013) Robust stabilization of singular Markovian jump systems with uncertain switching. International Journal of Control, Automation, and Systems11(1): 188–193.
29.
WillemsJC (1972a) Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis45(5): 321–351.
30.
WillemsJC (1972b) Dissipative dynamical systems part II: Linear systems with quadratic supply rates. Archive for Rational Mechanics and Analysis45(5): 352–393.
31.
WuZGParkJHSuHY. (2011) Dissipativity analysis for singular systems with time-varying delays. Applied Mathematics and Computation218(8): 4605–4613.
32.
WuZGParkJHSuHY. (2012) Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties. Nonlinear Dynamics69(3): 1323–1332.
33.
XiongJLLamJ (2009) Robust H2 control of Markovian jump systems with uncertain switching probabilities. International Journal of Systems Science40(3): 255–265.
34.
XiongJLLamJGaoHJ. (2005) On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica41(5): 897–903.
35.
YangDZhaoJ (2015) Robust finite-time output feedback H∞ control for stochastic jump systems with incomplete transition rates. Circuits, Systems, and Signal Processing34(6): 1799–1824.
36.
ZhangHGuanZHFengG (2008) Reliable dissipative control for stochastic impulsive systems. Automatica44(4): 1004–1010.
37.
ZhangLXBoukasEK (2009) Stability and stabilization for Markovian jump linear systems with partly unknown transition probabilities. Automatica45(2): 463–468.
ZhangYQLiuCXSongYD (2013) Finite-time H∞ filtering for discrete-time Markovian jump systems. Journal of the Franklin Institute350(6): 1579–1595.
40.
ZhaoJJShenHLiB. (2013) Finite-time H∞ control for a class of Markovian jump delayed systems with input saturation. Nonlinear Dynamics73(1–2): 1099–1110.
41.
ZhaoJJWangJParkJH. (2015) Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates. Nonlinear Analysis: Hybrid Systems15: 52–62.
