Passive control for singular time-delay system with actuator saturation

This paper considers the problem of passivity controller design for singular time-delay system with actuator saturation and nonlinear disturbance. Firstly, by tuning the Wirtinger-based integral inequality, a sufficient condition is derived to guarantee that the nonlinear singular time-delay system is regular, impulse free, asymptotically stable with the dissipation performance. Then, based on the derived condition, and applying linear matrix inequalities(LMIs) techniques, the passive state feedback controller is synthesized. Moreover, the maximal estimate of the domain of attraction is proposed by an optimization problem. Finally, some numerical examples are given to illustrate the effectiveness of the obtained theoretic results.

[1]  Ju H. Park,et al.  Reliable passive control for singular systems with time-varying delays , 2013 .

[2]  Zhengrong Xiang,et al.  Stability, l1-gain and l∞-gain analysis for discrete-time positive switched singular delayed systems , 2016, Appl. Math. Comput..

[3]  Song Zhu,et al.  Passivity analysis of stochastic delayed neural networks with Markovian switching , 2011, Neurocomputing.

[4]  Xun-lin Zhu,et al.  Delay-dependent Stability Criteria for Singular Time-delay Systems , 2010 .

[5]  E. Tissir,et al.  Delay dependent robust stability of singular systems with time-varying delay , 2012 .

[6]  Hao Shen,et al.  Mixed H∞/passive synchronization for complex dynamical networks with sampled-data control , 2015, Appl. Math. Comput..

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

[8]  Hao Shen,et al.  Finite-time asynchronous H∞ control for Markov jump repeated scalar non-linear systems with input constraints , 2016, Appl. Math. Comput..

[9]  Hao Shen,et al.  Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Rathinasamy Sakthivel,et al.  Robust reliable sampled-data H∞ control for uncertain stochastic systems with random delay , 2015, Complex..

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

[12]  Yonggang Chen,et al.  Stabilization of neutral time-delay systems with actuator saturation via auxiliary time-delay feedback , 2015, Autom..

[13]  James Lam,et al.  New admissibility analysis for discrete singular systems with time-varying delay , 2015, Appl. Math. Comput..

[14]  Hamid Reza Karimi,et al.  On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems , 2014, J. Frankl. Inst..

[15]  E. Fridman,et al.  H∞-control of linear state-delay descriptor systems: an LMI approach , 2002 .

[16]  Qin Li,et al.  Robust Passive Control for Uncertain Time-Delay Singular Systems , 2009, IEEE Trans. Circuits Syst. I Regul. Pap..

[17]  Pin-Lin Liu,et al.  Further improvement on delay-range-dependent stability results for linear systems with interval time-varying delays. , 2013, ISA transactions.

[18]  Hanyong Shao.  Further improvement on delay-dependent stability results for linear systems with time-varying delays , 2011, Proceedings of the 30th Chinese Control Conference.

[19]  Jun Song,et al.  Finite-time robust passive control for a class of uncertain Lipschitz nonlinear systems with time-delays , 2015, Neurocomputing.

[20]  Chenghui Zhang,et al.  H∞ control for discrete-time singular Markov jump systems subject to actuator saturation , 2012, J. Frankl. Inst..

[21]  Wang Xiaofeng,et al.  H∞ control for linear systems with interval time-varying delay , 2013, Proceedings of the 32nd Chinese Control Conference.

[22]  Jin-Hoon Kim,et al.  Note on stability of linear systems with time-varying delay , 2011, Autom..

[23]  Yonggui Kao,et al.  Stabilisation of mode-dependent singular Markovian jump systems with generally uncertain transition rates , 2014, Appl. Math. Comput..

[24]  Ju H. Park,et al.  Stability of time-delay systems via Wirtinger-based double integral inequality , 2015, Autom..

[25]  Zongli Lin,et al.  Set Invariance Conditions for Singular Linear Systems Subject to Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[26]  Junqiang Xi,et al.  Special Issue on “Recent Developments on Modeling and Control of Hybrid Electric Vehicles” , 2016 .

[27]  E. Fridman.  Stability of linear descriptor systems with delay: a Lyapunov-based approach , 2002 .

[28]  Hanyong Shao,et al.  Improved delay-dependent stability criteria for systems with a delay varying in a range , 2008, Autom..

[29]  Qingling Zhang,et al.  Delay-dependent H-infinity control for linear descriptor systems with delay in state , 2005 .

[30]  Yuechao Ma,et al.  Robust guaranteed cost H∞ control for singular systems with multiple time delays subject to input saturation , 2015, J. Syst. Control. Eng..

[31]  V. Singh.  Robust stability of cellular neural networks with delay: linear matrix inequality approach , 2004 .

[32]  Rathinasamy Sakthivel,et al.  Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays , 2015 .

[33]  Dong Xin.  Robust passive control for singular systems with time-varying uncertainties , 2004 .

[34]  Renxin Zhong,et al.  DELAY‐DEPENDENT ROBUST CONTROL OF DESCRIPTOR SYSTEMS WITH TIME DELAY , 2006 .

[35]  Qin Li,et al.  Robust Passive Control for Uncertain Time-Delay Singular Systems , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  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).

[37]  Qing-Long Han,et al.  On Hinfinity control for linear systems with interval time-varying delay , 2005, Autom..

[38]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[39]  Guoliang Wang,et al.  Stochastic stabilization of singular systems with Markovian switchings , 2015, Appl. Math. Comput..

[40]  Rathinasamy Sakthivel,et al.  Mixed H∞ and passive control for singular Markovian jump systems with time delays , 2015, J. Frankl. Inst..

[41]  Ju H. Park,et al.  Reliable mixed passive and ℋ∞ filtering for semi‐Markov jump systems with randomly occurring uncertainties and sensor failures , 2015 .

[42]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[43]  Hanyong Shao,et al.  New delay-dependent stability criteria for systems with interval delay , 2009, Autom..

[44]  Peng Shi,et al.  Reliable Mixed $H_\infty $ and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures , 2015, IEEE Transactions on Cybernetics.