Robust finite-time stabilization for positive delayed semi-Markovian switching systems

Abstract Robust finite-time stabilization is discussed for positive semi-Markovian switching systems (S-MSSs), in which semi-Markovian process, time-varying delay, external disturbance, and transient performance in finite-time level are all considered in a unified framework. In the system under consideration, finite-time problem can describe transient performance of practical control process. Firstly, some finite-time boundedness and L 1 finite-time boundedness criteria for positive delayed S-MSSs are proposed by constructing the stochastic semi-Markovian Lyapunov–Krasovskii functional with mode-dependent integral term. Then, a developed L 1 finite-time feedback controller design method is presented to reduce some constraints of input matrices, which guarantees the resulting closed-loop system achieves positivity, finite-time boundedness, and has a prescribed L 1 noise attenuation performance index in a novel standard linear programming. Finally, a practical example is illustrated to validate the proposed results by applying a virus mutation treatment model.

[1]  Patrizio Colaneri,et al.  Stochastic stability of Positive Markov Jump Linear Systems , 2014, Autom..

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

[3]  Shihua Li,et al.  Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Mismatched Term , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[4]  Yang Tang,et al.  Stability Analysis of Stochastic Delayed Systems With an Application to Multi-Agent Systems , 2016, IEEE Transactions on Automatic Control.

[5]  Xiaoming Chen,et al.  Dynamic output-feedback control for continuous-time interval positive systems under L1 performance , 2016, Appl. Math. Comput..

[6]  Jie Lian,et al.  Mean Stability of Positive Markov Jump Linear Systems With Homogeneous and Switching Transition Probabilities , 2015, IEEE Transactions on Circuits and Systems II: Express Briefs.

[7]  T. Kaczorek.  Positive 1D and 2D Systems , 2001 .

[8]  Jun Shen,et al.  Reset stabilisation of positive linear systems , 2016, Int. J. Syst. Sci..

[9]  Jianbin Qiu,et al.  Sliding mode control for semi-Markovian jump systems via output feedback , 2017, Autom..

[10]  Qingling Zhang,et al.  L1 fuzzy observer design for nonlinear positive Markovian jump system , 2018 .

[11]  Dimitri Peaucelle,et al.  Analysis and Synthesis of Interconnected Positive Systems , 2017, IEEE Transactions on Automatic Control.

[12]  Wenhai Qi,et al.  $$L_1$$L1 Control for Positive Markovian Jump Systems with Time-Varying Delays and Partly Known Transition Rates , 2015, Circuits Syst. Signal Process..

[13]  Renquan Lu,et al.  Prescribed Performance Observer-Based Adaptive Fuzzy Control for Nonstrict-Feedback Stochastic Nonlinear Systems , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[14]  W. Zheng,et al.  Finite‐time H ∞  control for discrete‐time switched nonlinear systems with time delay , 2015 .

[15]  James Lam,et al.  Stability and Performance Analysis for Positive Fractional-Order Systems With Time-Varying Delays , 2016, IEEE Transactions on Automatic Control.

[16]  Hao Shen,et al.  A Markov jump model approach to reliable event-triggered retarded dynamic output feedback H∞ control for networked systems , 2017 .

[17]  Qing-Long Han,et al.  I1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach , 2014, Autom..

[18]  Yafeng Guo,et al.  Stabilization of positive Markov jump systems , 2016, J. Frankl. Inst..

[19]  Yonggui Kao,et al.  Passification of Uncertain Singular Semi-Markovian Jump Systems With Actuator Failures Via Sliding Mode Approach , 2017, IEEE Transactions on Automatic Control.

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

[21]  Zhengzhi Han,et al.  L1/ℓ1-Gain analysis and synthesis of Markovian jump positive systems with time delay. , 2016, ISA transactions.

[22]  Linlin Hou,et al.  Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities , 2018, Autom..

[23]  Shengyuan Xu,et al.  On Stability of a Class of Switched Nonlinear Systems Subject to Random Disturbances , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Hao Shen,et al.  Event-triggered dissipative filtering for networked semi-Markov jump systems and its applications in a mass-spring system model , 2017 .

[25]  Ying-Xu Yang,et al.  Finite‐time stability of switched positive linear systems , 2014 .

[26]  Franco Blanchini,et al.  Discrete‐time control for switched positive systems with application to mitigating viral escape , 2011 .

[27]  Hangli Ren,et al.  Finite-time stability of interconnected impulsive switched systems , 2016 .

[28]  James Lam,et al.  $\ell_{\infty}/L_{\infty} $-Gain Analysis for Positive Linear Systems With Unbounded Time-Varying Delays , 2015, IEEE Transactions on Automatic Control.

[29]  F. Tadeo,et al.  Controller Synthesis for Positive Linear Systems With Bounded Controls , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Hong Wang,et al.  Stabilization of chaotic systems under variable sampling and state quantized controller , 2017, Fuzzy Sets Syst..

[31]  Guoliang Chen,et al.  Extended dissipative analysis of generalized Markovian switching neural networks with two delay components , 2017, Neurocomputing.

[32]  Claudio Altafini,et al.  Minimal eventually positive realizations of externally positive systems , 2016, Autom..

[33]  Hamid Reza Karimi,et al.  $\mathscr {L}_\infty$ Control for Positive Delay Systems With Semi-Markov Process and Application to a Communication Network Model , 2019, IEEE Transactions on Industrial Electronics.

[34]  Patrizio Colaneri,et al.  Stability and Stabilization of Discrete-Time Semi-Markov Jump Linear Systems via Semi-Markov Kernel Approach , 2016, IEEE Transactions on Automatic Control.

[35]  Jun Cheng,et al.  Fuzzy-model-based H∞ control for discrete-time switched systems with quantized feedback and unreliable links , 2018, Inf. Sci..

[36]  Michael V. Basin,et al.  Observer-Based Composite Adaptive Fuzzy Control for Nonstrict-Feedback Systems With Actuator Failures , 2018, IEEE Transactions on Fuzzy Systems.

[37]  Guoliang Chen,et al.  ℓ2 Gain Analysis and State Feedback Stabilization of Switched Systems with Multiple Additive Time-varying Delays , 2017, J. Frankl. Inst..

[38]  Zhengzhi Han,et al.  Stochastic stability and stabilization of positive systems with Markovian jump parameters , 2014 .

[39]  Hamid Reza Karimi,et al.  Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems , 2018, IEEE Transactions on Fuzzy Systems.

[40]  Hamid Reza Karimi,et al.  A Flexible Terminal Approach to Sampled-Data Exponentially Synchronization of Markovian Neural Networks With Time-Varying Delayed Signals , 2018, IEEE Transactions on Cybernetics.

[41]  Yonggui Kao,et al.  Anti-windup design for stochastic Markovian switching systems with mode-dependent time-varying delays and saturation nonlinearity , 2017 .

[42]  Chuangyin Dang,et al.  Stability Analysis of Positive Switched Linear Systems With Delays , 2011, IEEE Transactions on Automatic Control.

[43]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[44]  Yang Shi,et al.  Stochastic stability and robust stabilization of semi‐Markov jump linear systems , 2013 .

[45]  Jing Wang,et al.  Mixed H∞ /passive sampled-data synchronization control of complex dynamical networks with distributed coupling delay , 2017, J. Frankl. Inst..

[46]  Jing Wang,et al.  Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback , 2018, Appl. Math. Comput..

[47]  Wei Xing Zheng,et al.  Second-Order Sliding-Mode Controller Design and Its Implementation for Buck Converters , 2018, IEEE Transactions on Industrial Informatics.

[48]  Wenhai Qi,et al.  Observer-Based Adaptive SMC for Nonlinear Uncertain Singular Semi-Markov Jump Systems With Applications to DC Motor , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[49]  Tieshan Li,et al.  Event-Triggered Finite-Time Control for Networked Switched Linear Systems With Asynchronous Switching , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[50]  Dan Ye,et al.  Fault-Tolerant Controller Design for General Polynomial-Fuzzy-Model-Based Systems , 2018, IEEE Transactions on Fuzzy Systems.

[51]  Hamid Reza Karimi,et al.  New approaches to positive observer design for discrete-time positive linear systems , 2018, J. Frankl. Inst..