This paper deals with the problem of passivity and passification for stochastic Markovian jump systems with incomplete transition rates and actuator saturation. By use of the polytopic model, sufficient conditions are built such that the closed-loop constrained system is stochastically passive. The procedure of deriving a state feedback controller is converted into an optimization problem with a set of linear matrix inequalities. Finally, the simulation results of a linearized dynamic model of a vertical take-off and landing aircraft in the vertical plane illustrate the effectiveness of the proposed schemes.
ShenHParkJHWuZG. Finite-time synchronization control for uncertain Markov jump neural networks with input constraints. Nonlinear Dyn2014; 77(4): 1709–1720.
2.
MaoXR. Stability of stochastic differential equations with Markovian switching. Stoch Proc Appl1999; 79(1): 45–67.
3.
De FariasDPGeromelJCDo ValJBR. Output feedback control of Markov jump linear systems in continuous time. IEEE Trans Automat Control2000; 45(5): 944–949.
4.
KaoYGXieJWangCH. Stabilisation of singular Markovian jump systems with generally uncertain transition rates. IEEE Trans Automat Control2014; 59(9): 2604–2610.
5.
KaoYGXieJWangCH. A sliding mode approach to H∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems. Automatica2015; 52: 218–226.
6.
DingYLiuHChengJ. H∞ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays. ISA T2014; 53(4): 1054–1060.
7.
ChengJZhuHZhongS. Finite-time H∞ estimation for discrete-time Markov jump systems with time-varying transition probabilities subject to average dwell time switching. Commun Nonlinear Sci2015; 20(2): 571–582.
8.
ChengJZhuHDingY. Stochastic finite-time boundedness for Markovian jumping neural networks with time-varying delays. Appl Math Comput2014; 242: 281–295.
9.
ChengJZhuHZhongS. Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. ISA T2013; 52(6): 768–774.
10.
ZhangLBoukasEK. Stability and stabilization for Markovian jump linear systems with partly unknown transition probabilities. Automatica2009; 45(2): 463–468.
11.
ZhaoJWangJShenH. Dynamic anti-windup control design for Markovian jump delayed systems with input saturation. Circ Syst Signal Pr2013; 32(5): 2213–2229.
12.
ZhaoJWangJParkJH. Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates. Nonlinear Anal: Hybrid Syst2015; 15: 52–62.
13.
WangYZuoZCuiY. Stochastic stabilization of Markovian jump systems with partially unknown transition probabilities and actuator saturation. Circ Syst Signal Pr2012; 31(1): 371–383.
14.
DingYZhuHZhongS. H∞ filtering for stochastic systems with Markovian switching and partly unknown transition probabilities. Circ Syst Signal Pr2013; 32(2): 559–583.
15.
ChenYZhengWX. Exponential H∞ filtering for stochastic Markovian jump systems with time delays. Int J Robust Nonlin2014; 24(4): 625–643.
16.
WangGL. Stochastic stabilization of singular systems with Markovian switchings. Appl Math Comput2015; 250: 390–401.
17.
XieLHeXZhangW. Robust H∞ control for uncertain stochastic saturating systems with time delays. J Syst Eng Electron2004; 15(4): 563–567.
18.
CaoYLinZL. Stability analysis of discrete-time systems with actuator saturation by a saturation dependent Lyapunov function. Automatica2003; 39(7): 1235–1242.
19.
GrimmGHatfieldJPostlethwaiteI. Antiwindup for stable linear systems with input saturation: an LMI based synthesis. IEEE Trans Automat Control2003; 48(9): 1509–1525.
20.
WuFGrigoriadisKMPackardA. Anti-windup controller design using linear parameter-varying control methods. Int J Control2000; 73(12): 1104–1114.
21.
DeyRGhoshSRayG. Improved delay-dependent stabilization of time-delay systems with actuator saturation. Int J Robust Nonlin2014; 24(5): 902–917.
22.
LiuHPBoukasEKSunFC. Controller design for Markov jump systems subject to actuator saturation. Automatica2006; 42(3): 459–465.
23.
RaoufJBoukasEK. Stabilization of singular Markovian jump systems with discontinuities and saturating inputs. J Optim Theory Appl2009; 143(2): 369–389.
24.
WuZGParkJHSuHY. Reliable passive control for singular systems with time-varying delays. J Process Control2013; 23(8): 1217–1228.
25.
WenSPZengZGHuangTW. Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays. Int J Robust Nonlin2015; 25(4): 610–624.
26.
WangYGuptaVAntsaklisPJ. On passivity of a class of discrete-time switched nonlinear systems. IEEE Trans Automat Control2014; 59(3): 692–702.
27.
WuYHGuanZHFengG. Passivity-based control of hybrid impulsive and switching systems with singular structure. J Franklin Inst2013; 350(6): 1500–1512.
28.
YaoXMGuoL. Composite disturbance-observer-based output feedback control and passive control for Markovian jump systems with multiple disturbances. IET Control Theory A2014; 8(10): 873–881.
29.
HeSPLiuF. Optimal finite-time passive controller design for uncertain nonlinear Markovian jumping systems. J Franklin Inst2014; 351(7): 3782–3796.
30.
RezaKH. Passivity-based output feedback control of Markovian jump systems with discrete and distributed time-varying delays. Int J Syst Sci2013; 44(7): 1290–1300.
31.
WangYYWangQBZhouPF. Delay-dependent passivity and passification for uncertain singularly perturbed Markovian jump systems with time-varying delay. Circ Syst Signal Pr2012; 31(6): 2179–2194.
