Passive gain-scheduling filtering for jumping linear parameter varying systems with fading channels based on the hidden Markov model

Abstract

This work is aimed to address the passive gain-scheduling filtering problem for Markov jump linear parameter varying systems with fading channels. A hidden Markov process is employed to describe mode information exchange between the system and the presented filter. By the aid of stochastic analysis theory, some sufficient conditions for guaranteeing the existence of an available passive gain-scheduling filter are established. On the basis of the designed filter, the passivity of the filtering error system is ensured in the presence of randomly occurring fading channels. Finally, an explained example is put forward to verify the effectiveness of the filter.

Keywords

Jumping linear parameter varying systems fading channels passive gain-scheduling filtering hidden Markov model

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References

Shamma

JS.

Analysis and design of gain scheduled control systems. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1988.

Chen

Xia

Zhuang

et al . Improved delay-dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components. Appl Math Comput 2018; 316: 1–17.

Shamma

Athans

Analysis of gain scheduled control for nonlinear plants. IEEE T Automat Contr 1990; 35(8): 898–907.

Chen

Xia

Zhuang

et al .

l_{2}

gain analysis and state feedback stabilization of switched systems with multiple additive time-varying delays. J Frankl Inst 2017; 354(16): 7326–7345.

Shamma

Athans

Guaranteed properties of gain scheduled control for linear parameter-varying plants. Automatica 1991; 27(3): 559–564.

Lee

Shin

Chung

MJ.

A design of gain-scheduled control for a linear parameter varying system: an application to flight control. Control Eng Pract 2001; 9(1): 11–21.

Papageorgiou

Glover

D’Mello

et al . Taking robust LPV control into flight on the VAAC Harrier. In: Proceedings of the 39th IEEE conference on decision and control, Sydney, NSW, Australia, 12–15 December 2000, vol. 5, pp.4558–4564. New York: IEEE.

Leith

Leithead

. Gain-scheduled control of a skid-to-turn missile: relaxing slow variation requirements by velocity-based design. In: Proceedings of the American control conference, Arlington, VA, 25–27 June 2001, vol. 1, pp.500–505. New York: IEEE.

Rugh

Shamma

JS.

Research on gain scheduling. Automatica 2000; 36(10): 1401–1425.

10.

Zong

Wang

Zheng

et al . Finite-time stabilization for a class of switched time-delay systems under asynchronous switching. Appl Math Comput 2013; 219(11): 5757–5771.

11.

Miyasato

. Adaptive gain-scheduled

H_{\infty}

control of linear parameter-varying systems with nonlinear components. In: Proceedings of the American control conference, Denver, Colorado, United States, 4–6 June 2003, July 2003, vol. 1, pp.208–213. New York: IEEE.

12.

Zong

Wang

Zheng

et al . Finite-time

H_{\infty}

control for discrete-time switched nonlinear systems with time delay. Int J Robust Nonlin 2015; 25(6): 914–936.

13.

Xia

Gao

Liu

et al . Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems. J Frankl Inst 2018; 355: 3031–3049.

14.

Shen

Z-G

et al . Reliable dissipative control for Markov jump systems using an event-triggered sampling information scheme. Nonlinear Anal: Hybri 2017; 25: 41–59.

15.

Shi

et al . Finite-time distributed state estimation over sensor networks with round-robin protocol and fading channels. IEEE T Cybernetics 2018; 48(1): 336–345.

16.

Shen

Dai

Yan

et al . Quantized output feedback control for stochastic semi-Markov jump systems with unreliable links. IEEE T Circuits-II 2018; 65: 1998–2002.

17.

Liang

Dai

Shen

et al .

l_{2} - l_{\infty}

synchronization for singularly perturbed complex networks with semi-Markov jump topology. Appl Math Comput 2018; 321: 450–462.

18.

Shi

et al . Robust estimation for neural networks with randomly occurring distributed delays and Markovian jump coupling. IEEE T Neur Net Lear 2018; 29: 845–855.

19.

Xia

Chen

Sun

Extended dissipative analysis of generalized Markovian switching neural networks with two delay components. Neurocomputing 2017; 260: 275–283.

20.

Shen

Huang

Zhou

et al . Global exponential estimates for uncertain Markovian jump neural networks with reaction-diffusion terms. Nonlinear Dynam 2012; 69(1–2): 473–486.

21.

Men

Huang

Wang

et al . Quantized asynchronous dissipative state estimation of jumping neural networks subject to occurring randomly sensor saturations. Neurocomputing 2018; 291: 207–214.

22.

Shen

et al . Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE T Automat Contr 2018; 63: 2709–2714.

23.

Wang

Yao

et al . State estimation for periodic neural networks with uncertain weight matrices and Markovian jump channel states. IEEE T Syst Man Cy-S 2018; 48: 1841–1850.

24.

Wang

Liang

Huang

et al . Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback. Appl Math Comput 2018; 328: 247–262.

25.

Shen

Huo

Cao

et al . Generalized state estimation for Markovian coupled networks under round-robin protocol and redundant channels. IEEE T Cybernetics. Epub ahead of print 12 February 2018. DOI: 10.1109/TCYB.2018.2799929.

26.

Zong

Yang

Hou

et al . Robust finite-time

H_{\infty}

control for Markovian jump systems with partially known transition probabilities. J Frankl Inst 2013; 350(6): 1562–1578.

27.

Shen

Zhu

Zhang

et al . Extended dissipative state estimation for Markov jump neural networks with unreliable links. IEEE T Neur Net Lear 2017; 28(2): 346–358.

28.

Chen

Xia

Zhuang

Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components. J Frankl Inst 2016; 353(9): 2137–2158.

29.

Shen

Men

Z-G

et al . Nonfragile

H_{\infty}

control for fuzzy Markovian jump systems under fast sampling singular perturbation. IEEE T Syst Man Cy-S 2018; 48: 2058–2069.

30.

Shen

Yan

et al . Finite-time event-triggered

H_{\infty}

control for T-S fuzzy Markov jump systems. IEEE T Fuzzy Syst 2018; 26: 3122–3135.

31.

Shen

Z-G

Shi

et al . Dissipativity-based asynchronous filtering for periodic Markov jump systems. Inform Sciences 2017; 420: 505–516.

32.

Zhu

Zhong

Zheng

et al . HMM-based

H_{\infty}

filtering for discrete-time Markov jump LPV systems over unreliable communication channels. IEEE T Syst Man Cy-S 2018; 48: 2035–2046.

33.

Meisami-Azad

Mohammadpour

Grigoriadis

KM.

Dissipative analysis and control of state-space symmetric systems. Automatica 2009; 45(6): 1574–1579.

34.

Karimi

Duffie

Dashkovskiy

Local capacity

H_{\infty}

control for production networks of autonomous work systems with time-varying delays. IEEE T Autom Sci Eng 2010; 7(4): 849–857.

35.

Gao

Karimi

HR.

Stability analysis and

H_{\infty}

controller synthesis of discrete-time switched systems with time delay. Syst Control Lett 2014; 66: 85–93.

36.

Karimi

Jabedar Maralani

Lohmann

et al .

H_{\infty}

control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions. Int J Control 2005; 78(4): 254–263.

37.

Wang

et al . Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays. Appl Math Comput 2018; 330: 152–169.

38.

Wang

et al . Stability and Hopf bifurcation of fractional-order complex-valued single neuron model with time delay. Int J Bifurcat Chaos 2017; 27(13): 1750209.

39.

Wang

A numerical method for delayed fractional-order differential equations. J Appl Math 2013; 2013: 256071.

40.

Wang

Huang

Zhou

A numerical method for delayed fractional-order differential equations: based on G-L definition. Appl Math Inform Sci 2013; 7(2): 525–529.

41.

Wang

Huang

Shi

Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay. Comput Math Appl 2011; 62(3): 1531–1539.

42.

Zhang

Shao

Wang

et al . Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems. Appl Math Comput 2012; 218(14): 7614–7621.

43.

Gao

Xia

Zhuang

et al . Nonfragile finite-time extended dissipative control for a class of uncertain switched neutral systems. Complexity 2017; 2017: 6581308.

44.

Liu

Wei

et al . New insight into reachable set estimation for uncertain singular time-delay systems. Appl Math Comput 2018; 320: 769–780.

45.

Kao

Gao

et al . Controller design for time-delay system with stochastic disturbance and actuator saturation via a new criterion. Appl Math Comput 2018; 320: 535–546.

46.

Zhou

Sang

et al .

H_{\infty}

consensus for nonlinear stochastic multi-agent systems with time delay. Appl Math Comput 2018; 325: 41–58.

47.

Wei

Qiu

Karimi

HR.

Reliable output feedback control of discrete-time fuzzy affine systems with actuator faults. IEEE T Circuits-I 2017; 64(1): 170–181.

48.

Qiu

Wei

Karimi

et al . Reliable control of discrete-time piecewise-affine time-delay systems via output feedback. IEEE T Reliab 2018; 67: 79–91.