Mean square exponential stabilization of sampled‐data Markovian jump systems

Funding information National Natural Science Foundation of China, Grant/Award Number: 61522303, U1509215 and 61621063; ChangJiang Scholars Program; National Outstanding Youth Talents Support Program; Program for Changjiang Scholars and Innovative Research Team in University , Grant/Award Number: IRT1208; Program for New Century Excellent Talents in University, Grant/Award Number: NCET-13-0045 Summary In this paper, the problem of mean square exponential stabilization for sampled-data Markovin jump systems is studied. A time-scheduled Lyapunov functional consisting of a exponential-type looped function is constructed using segmentation technology and linear interpolation. Based on this new Lyapunov functional, a less conservative mean square exponential stability criterion is obtained such that a bigger maximum decay rate can be easily calculated. Meanwhile, the quantitative relationship among some system parameters, maximum sampling period, and decay rate is established. Moreover, a time-dependent state feedback sample-data controller is designed. Significant improvements of the proposed exponential-type time-scheduled Lyapunov functional method over some existing ones are verified by numerical examples.

[1]  Khashayar Khorasani,et al.  A Decentralized Markovian Jump ${\cal H}_{\infty}$ Control Routing Strategy for Mobile Multi-Agent Networked Systems , 2011, IEEE Transactions on Control Systems Technology.

[2]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[3]  James Lam,et al.  Further Results on Exponential Estimates of Markovian Jump Systems With Mode-Dependent Time-Varying Delays , 2011, IEEE Transactions on Automatic Control.

[4]  Qing-Long Han,et al.  Event-based H∞ filtering for sampled-data systems , 2015, Autom..

[5]  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.

[6]  Qing-Long Han,et al.  A Decentralized Event-Triggered Dissipative Control Scheme for Systems With Multiple Sensors to Sample the System Outputs , 2016, IEEE Transactions on Cybernetics.

[7]  D. Sworder,et al.  Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria , 1975 .

[8]  Patrizio Colaneri,et al.  Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time , 2010, Autom..

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

[10]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[11]  K. Åström,et al.  Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems , 1999 .

[12]  Shihua Li,et al.  Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control , 2018 .

[13]  Hamid Reza Karimi,et al.  Resilient Sampled-Data Control for Markovian Jump Systems With an Adaptive Fault-Tolerant Mechanism , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  Joao P. Hespanha,et al.  Tracking control for sampled‐data systems with uncertain time‐varying sampling intervals and delays , 2009 .

[15]  Corentin Briat,et al.  Stability analysis of uncertain sampled-data systems with incremental delay using looped-functionals , 2015, Autom..

[16]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[17]  Peng Shi,et al.  Local Synchronization of Chaotic Neural Networks With Sampled-Data and Saturating Actuators , 2014, IEEE Transactions on Cybernetics.

[18]  Peng Shi,et al.  Extended sliding mode observer based control for Markovian jump linear systems with disturbances , 2016, Autom..

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

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

[21]  Shengyuan Xu,et al.  Robust stabilization of Markovian delay systems with delay-dependent exponential estimates , 2006, Autom..

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

[23]  Qing-Long Han,et al.  Observer‐based H ∞  output tracking control for networked control systems , 2014 .

[24]  Lihua Xie,et al.  Mean square stability for Kalman filtering with Markovian packet losses , 2011, Autom..

[25]  José Claudio Geromel,et al.  Optimal H2 state feedback sampled-data control design of Markov Jump Linear Systems , 2015, Autom..

[26]  M. Fragoso,et al.  Continuous-Time Markov Jump Linear Systems , 2012 .

[27]  Weiming Xiang,et al.  Mode-identifying time estimation and switching-delay tolerant control for switched systems: An elementary time unit approach , 2016, Autom..

[28]  Gang Feng,et al.  Stability and Stabilization of Markovian Jump Systems With Time Delay Via New Lyapunov Functionals , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Weiming Xiang.  Necessary and Sufficient Condition for Stability of Switched Uncertain Linear Systems Under Dwell-Time Constraint , 2016, IEEE Transactions on Automatic Control.

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

[31]  E. Fridman,et al.  Networked‐based stabilization via discontinuous Lyapunov functionals , 2012 .

[32]  Ian R. Petersen,et al.  Finite horizon H∞ control for a class of sampled‐data linear quantum systems , 2017 .

[33]  Paulo Tabuada,et al.  An introduction to event-triggered and self-triggered control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[34]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[35]  Hao Shen,et al.  Robust extended dissipative control for sampled-data Markov jump systems , 2014, Int. J. Control.

[36]  Renquan Lu,et al.  Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling , 2015, Syst. Control. Lett..

[37]  ShiPeng,et al.  Asynchronous l 2 - l ∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014 .

[38]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[39]  Hisaya Fujioka,et al.  A Discrete-Time Approach to Stability Analysis of Systems With Aperiodic Sample-and-Hold Devices , 2009, IEEE Transactions on Automatic Control.

[40]  Jian Sun,et al.  Stability Analysis of Networked Control Systems With Aperiodic Sampling and Time-Varying Delay. , 2017, IEEE transactions on cybernetics.

[41]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[42]  Chung-Yao Kao.  An IQC Approach to Robust Stability of Aperiodic Sampled-Data Systems , 2016, IEEE Transactions on Automatic Control.

[43]  Uri Shaked,et al.  Robust stability and stabilization of linear switched systems with dwell time , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[44]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[45]  Peng Shi,et al.  Robust sampled-data control for Markovian jump linear systems , 2006, Autom..

[46]  José Claudio Geromel,et al.  Performance evaluation of sampled-data control of Markov jump linear systems , 2017, Autom..

[47]  Weihai Zhang,et al.  Finite-Time Stability and Stabilization of Itô Stochastic Systems With Markovian Switching: Mode-Dependent Parameter Approach , 2015, IEEE Transactions on Automatic Control.

[48]  Constantino M. Lagoa,et al.  Set membership identification of switched linear systems with known number of subsystems , 2015, Autom..

[49]  Wen-an Zhang,et al.  Stabilization of Sampled-Data Control Systems With Control Inputs Missing , 2010, IEEE Transactions on Automatic Control.

[50]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[51]  Oscar R. González,et al.  Stability analysis of digital linear flight controllers subject to electromagnetic disturbances , 2000, IEEE Trans. Aerosp. Electron. Syst..

[52]  Fuwen Yang,et al.  An impulsive‐switched‐system approach to aperiodic sampled‐data systems with time‐delay control , 2018 .

[53]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.