The static output feedback control of continuous Markov jump systems with incomplete transition probabilities is investigated in this paper. Employing the property of continuous transition probabilities and a matrix transformation technique, relaxed sufficient conditions for the existence of a solution to the static output feedback control problem are established in terms of linear matrix inequalities. In addition, the obtained results are extended to Markov jump nonlinear systems. Numerical examples are provided to demonstrate the effectiveness of the derived results.
BoukasEK (2006) Static output feedback control for stochastic hybrid systems: LMI approach. Automatica42: 183–188.
2.
ChenBNiuYZouY (2013a) Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation. Automatica49: 1748–1754.
3.
ChenBNiuYZouY. (2013b) Reliable sliding-mode control for Markovian jumping systems subject to partial actuator degradation. Circuits, Systems, and Signal Processing32: 601–614.
4.
CostaOLVBenitesGRAM (2013) Robust mode-independent filtering for discrete-time Markov jump linear systems with multiplicative noises. International Journal of Control86: 779–793.
5.
CostaOLVdo ValJBRGeromelJC (1999) Continuous-time state-feedback H2-control of Markovian jump linear systems via convex analysis. Automatica35: 259–268.
6.
DongJYangG (2007) Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties. IEEE Transactions on Automatic Control54: 1930–1936.
7.
DongJYangG (2008) Robust H2 control of continuous-time Markov jump linear systems. Automatica44: 1431–1436.
8.
FengXLoparoKAJiY. (1992) Stochastic stability properties of jump linear systems. IEEE Transactions on Automatic Control37: 38–53.
9.
GarciaGPradinBZengF (2001) Stabilization of discrete time linear systems by static output feedback. IEEE Transactions on Automatic Control46: 1954–1958.
10.
HeSLiuF (2012) On robust controllability of uncertain non-linear jump systems with respect to the finite-time interval. Transactions of the Institute of Measurement and Control34: 841–849.
11.
JiYChizeckHJ (1990) Jump linear quadratic control: Steady state solution and testable conditions. Control Theory and Advanced Technology5: 289–319.
12.
KaranMShiPKayaCY (2006) Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica42: 2159–2168.
13.
LiuMHoDWCNiuY (2009) Stabilization of Markovian jump linear system over networks with random communication delay. Automatica45: 416–421.
14.
ShakedU (2003) An LPD approach to robust H2 and H∞ static output feedback design. IEEE Transactions on Automatic Control48: 866–872.
15.
ShenMYangG (2012a) H2 filter design for discrete-time Markov jump linear systems with partly unknown transition probabilities. Optimal Control Applications and Methods33: 318–337.
16.
ShenMYangG (2012b) New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities. IET Control Theory and Applications6: 2318–2325.
17.
ShenMYeD (2013) Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions. Fuzzy Sets and Systems217: 80–95.
18.
ShuZLamJXiongJ (2010) Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach. Automatica46: 687–694.
19.
SunMLamJXuS. (2012) Optimal time-weighted H2 model reduction for Markovian jump systems. International Journal of Control85: 613–628.
20.
SyrmosVLAbdallahCTGrigoriadisK (1997) Static output feedback – a survey. Automatica33: 125–137.
21.
TuanHApkarianPNarikiyoT. (2001) Parameterized linear matrix inequality techniques in fuzzy control system design. IEEE Transactions on Fuzzy Systems9: 324–332.
22.
WangGZhangQ (2012) Robust H∞ control of Markovian jump systems with uncertain switching probabilities. Asian Journal of Control14: 1159–1458.
23.
WangGZhangQSreeramV (2010) Partially mode-dependent H∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities. Signal Processing90: 548–556.
24.
WangGZhangQYangC (2013) Exponential H∞ filtering for singular systems with Markovian jump parameters. International Journal of Robust and Nonlinear Control23: 792–806.
25.
XiangWXiaoJ (2013) H∞ filtering for switched non-linear systems with polytopic uncertainties via filter state impulsive jump approach. Transactions of the Institute of Measurement and Control35: 540–550.
26.
XiaYBoukasEKShiP. (2009a) Stability and stabilization of continuous-time singular hybrid systems. Automatica45: 1504–1509.
27.
XiaYFuMShiP. (2009b) Adaptive backstepping controller design for stochastic jump systems. IEEE Transactions on Automatic Control54: 2853–2859.
28.
XiaYZhangJBoukasEK (2008) Control for discrete singular hybrid systems. Automatica44: 2635–2641.
29.
XiongJLamJ (2006) Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers. Automatica42: 747–753.
30.
XiongJLamJGaoH. (2005) On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica41: 897–903.
31.
XuSChenTLamJ (2003a) Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Transactions on Automatic Control48: 900–907.
32.
XuSLamJMaoX (2003b) Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Transactions on Circuits and Systems I: Regular Papers54: 2070–2077.
33.
ZhangBZhengWXuS (2012) Delay-dependent passivity and passification for uncertain Markovian jump systems with time-varying delays. International Journal of Robust and Nonlinear Control22: 1837–1852.
34.
ZhangLBoukasEK (2009a) Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica45: 463–468.
35.
ZhangLBoukasEK (2009b) H∞ control of a class of extended Markov jump linear systems. IET Control Theory and Applications3: 834–842.
36.
ZhangLBoukasEKLamJ (2008) Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities. IEEE Transactions on Automatic Control53: 2458–2464.
37.
ZhangYHeYWuM. (2011) Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices. Automatica47: 79–84.
