Decentralized Observer-Based Reliable Control for a Class of Interconnected Markov Jumped Time-Delay System Subject to Actuator Saturation and Failure

A decentralized stabilization method is investigated for a class of interconnected Markov jumping systems subject to time-varying delays, actuator saturation and jumped failure. The mean-square exponential stability condition is established by constructing multiple Lyapunov–Krasovskii functionals, which are delay-dependent, mode-dependent and decay rate-dependent. Taking into account the influence of actuator saturation and jumped actuator failure, decentralized observer-based $$ H_{\infty } $$H∞ state feedback stabilization schemes are designed. The decentralized observer gains and controller gains are determined by solving a convex optimization problem with $$ H_{\infty } $$H∞ performance $$ \gamma^{2} $$γ2 as objective and LMIs as constraints. Simulation results are also presented to illustrate the effectiveness and applicability of the obtained results.

[1]  Hui Liu,et al.  Stability analysis of continuous-time Markovian jump time-delay systems with time-varying transition rates , 2016, J. Frankl. Inst..

[2]  Zongli Lin,et al.  Output Feedback Stabilization of Linear Systems With Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[3]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

[4]  Ligang Wu,et al.  Fault Detection Filtering for Nonhomogeneous Markovian Jump Systems via a Fuzzy Approach , 2018, IEEE Transactions on Fuzzy Systems.

[5]  Christopher Edwards,et al.  Global decentralised static output feedback slidingmode control for interconnected time-delay systems , 2012 .

[6]  Lihua Xie,et al.  Stabilization of a class of uncertain large-scale stochastic systems with time delays , 2000, Autom..

[7]  N. Benhadj Braiek,et al.  Systematic linear matrix inequality conditions to design a robust decentralised observer-based optimal control for interconnected systems , 2012 .

[8]  Yonggui Kao,et al.  Stabilization for Positive Markovian Jump Systems with Actuator Saturation , 2017, Circuits Syst. Signal Process..

[9]  Magdi S. Mahmoud,et al.  Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays , 2009 .

[10]  Christopher Edwards,et al.  Decentralised stabilisation for nonlinear time delay interconnected systems using static output feedback , 2013, Autom..

[11]  Le Liu,et al.  Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation , 2017 .

[12]  G. P. Kladis,et al.  Stabilisation and Tracking for Swarm-Based UAV Missions Subject to Time-Delay , 2014 .

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  Xiao-Zheng Jin,et al.  Finite-time robust fault-tolerant control against actuator faults and saturations , 2017 .

[15]  Magdi S. Mahmoud,et al.  Interconnected jumping time‐delay systems: Mode‐dependent decentralized stability and stabilization , 2012 .

[16]  Weihai Zhang,et al.  Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach , 2011, Autom..

[17]  Weihua Gui,et al.  Event-Based Fault Detection Filtering for Complex Networked Jump Systems , 2018, IEEE/ASME Transactions on Mechatronics.

[18]  Peng Shi,et al.  Stochastic stability of Ito differential equations with semi-Markovian jump parameters , 2006, IEEE Transactions on Automatic Control.

[19]  Chun-xia Dou,et al.  Delay-dependent H∞ robust control for large power systems based on two-level hierarchical decentralised coordinated control structure , 2013, Int. J. Syst. Sci..

[20]  Shan Ma,et al.  Robust decentralized stabilization of Markovian jump large-scale systems: A neighboring mode dependent control approach , 2013, Autom..

[21]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[22]  Jin Bae Park,et al.  Decentralized Fuzzy Observer-Based Output-Feedback Control for Nonlinear Large-Scale Systems: An LMI Approach , 2014, IEEE Transactions on Fuzzy Systems.

[23]  Keum-Shik Hong,et al.  Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation , 2016 .

[24]  Yan-Ming Fu,et al.  Parametric method for spacecraft trajectory tracking control problem with stochastic thruster fault , 2016 .

[25]  Yang Shi,et al.  Active fault tolerant control systems by the semi‐Markov model approach , 2014 .

[26]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Zhou Gu,et al.  Stochastic faulty actuator‐based reliable control for a class of interval time‐varying delay systems with Markovian jumping parameters , 2011 .

[28]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[29]  Xunyuan Yin,et al.  Time-varying gain-scheduling σ -error mean square stabilisation of semi-Markov jump linear systems , 2016 .

[30]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[31]  Patrizio Colaneri,et al.  Stability and Stabilization of Semi-Markov Jump Linear Systems With Exponentially Modulated Periodic Distributions of Sojourn Time , 2017, IEEE Transactions on Automatic Control.

[32]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[33]  Shumin Fei,et al.  Decentralized $\mathcal{L}_{2}$–$\mathcal{L}_{\infty}$ Filtering for Interconnected Markovian Jump Systems with Delays , 2012, Circuits Syst. Signal Process..

[34]  Weihua Gui,et al.  Passivity-Based Asynchronous Sliding Mode Control for Delayed Singular Markovian Jump Systems , 2018, IEEE Transactions on Automatic Control.

[35]  Xin-Ping Guan,et al.  Exponential stabilization controller design for interconnected time delay systems , 2008, Autom..

[36]  Yuanqing Xia,et al.  A generalized approach to stabilization of linear interconnected time‐delay systems , 2012 .

[37]  Qingling Zhang,et al.  Robust observer-based passive control for uncertain singular time-delay systems subject to actuator saturation. , 2017, ISA transactions.

[38]  Sreten B. Stojanovic,et al.  Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Large Scale Time Delay Autonomous Systems , 2004 .

[39]  Lei Guo,et al.  Decentralized output-feedback adaptive control for a class of interconnected nonlinear systems with unknown actuator failures , 2016, Autom..

[40]  Dong Yue,et al.  Decentralized adaptive neural output feedback control of a class of large-scale time-delay systems with input saturation , 2015, J. Frankl. Inst..

[41]  Guang-Hong Yang,et al.  Decentralized fault detection and isolation of Markovian jump interconnected systems with unknown interconnections , 2017 .

[42]  Ligang Wu,et al.  Neural Network-Based Passive Filtering for Delayed Neutral-Type Semi-Markovian Jump Systems , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Ali Sghaier Tlili,et al.  Linear Matrix Inequality Robust Tracking Control Conditions for Nonlinear Disturbed Interconnected Systems , 2017 .

[44]  Ligang Wu,et al.  Stochastic stability of semi‐Markovian jump systems with mode‐dependent delays , 2014 .

[45]  Zhongzhi Hu,et al.  Decentralized stabilization of large scale interconnected systems with delays , 1994, IEEE Trans. Autom. Control..

[46]  Li Li,et al.  Decentralized robust control of uncertain Markov jump parameter systems via output feedback , 2006, 2006 American Control Conference.

[47]  Zhiqiang Zheng,et al.  Robust fault-tolerant control against time-varying actuator faults and saturation , 2012 .

[48]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[49]  Magdi S. Mahmoud,et al.  Resilient decentralized stabilization of interconnected time‐delay systems with polytopic uncertainties , 2011 .

[50]  Wenhai Qi,et al.  H∞ observer design for stochastic time-delayed systems with Markovian switching under partly known transition rates and actuator saturation , 2016, Appl. Math. Comput..

[51]  Engang Tian,et al.  Reliable control for interval time-varying delay systems subjected to actuator saturation and stochastic failure , 2012 .

[52]  V. Ugrinovskii *,et al.  Decentralized control of power systems via robust control of uncertain Markov jump parameter systems , 2005 .

[53]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[54]  Goshaidas Ray,et al.  Brief Paper: Stability analysis of interconnected time-delay systems in a generalised framework , 2010 .