Average dwell time approach to H∞ filter for continuous-time switched linear parameter varying systems with time-varying delay

Considering two types of delays including both time-varying delay and parameter varying delay in continuous switched linear parameter varying systems, the problem of H ∞ filtering under average dwell time switching is illustrated. The H ∞ filter depending on the linear time-varying parameter ρ ( t ) (mode-dependent parameterized filter) is designed at first. Then, based on multiple Lyapunov function and an improved reciprocally convex inequality, the corresponding existence sufficient conditions for the filter could ensure the obtained filter error system exponentially stable with a guaranteed H ∞ performance in the form of linear matrix inequalities. In addition, the designed filter gains under allowed switching signals are computed via the proposed convex optimal algorithm. In the end, two numerical examples show the effectiveness of the results in this work.

[1]  Peng Shi,et al.  H ∞ filtering for a class of switched linear parameter varying systems , 2011, Int. J. Syst. Sci..

[2]  Qingling Zhang,et al.  ' s personal copy Exponential H N filtering for time-varying delay systems : Markovian approach $ , 2011 .

[3]  Li Yu,et al.  Exponential stability analysis for neutral switched systems with interval time-varying mixed delays and nonlinear perturbations , 2012 .

[4]  Jianbin Qiu,et al.  A Novel Approach to Reliable Output Feedback Control of Fuzzy-Affine Systems With Time Delays and Sensor Faults , 2017, IEEE Transactions on Fuzzy Systems.

[5]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[6]  Wei Xing Zheng,et al.  Synchronization and State Estimation of a Class of Hierarchical Hybrid Neural Networks With Time-Varying Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[7]  Peng Shi,et al.  μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time , 2009, Int. J. Control.

[8]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[9]  Myeong-Jin Park,et al.  Generalized integral inequality: Application to time-delay systems , 2018, Appl. Math. Lett..

[10]  Hamid Reza Karimi,et al.  Fuzzy-Affine-Model-Based Memory Filter Design of Nonlinear Systems With Time-Varying Delay , 2018, IEEE Transactions on Fuzzy Systems.

[11]  Peng Shi,et al.  $H_\infty$ Filtering of Discrete-Time Switched Systems With State Delays via Switched Lyapunov Function Approach , 2007, IEEE Transactions on Automatic Control.

[12]  Yuanqing Xia,et al.  SMC Design for Robust Stabilization of Nonlinear Markovian Jump Singular Systems , 2018, IEEE Transactions on Automatic Control.

[13]  Jun Zhao,et al.  Output feedback variable structure control for a class of uncertain switched systems , 2009 .

[14]  Zidong Wang,et al.  Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis , 2007 .

[15]  Dan Zhang,et al.  Delay-dependent fault detection for switched linear systems with time-varying delays - the average dwell time approach , 2011, Signal Process..

[16]  Hamid Reza Karimi,et al.  Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Wei Xing Zheng,et al.  Dissipativity-Based Sliding Mode Control of Switched Stochastic Systems , 2013, IEEE Transactions on Automatic Control.

[18]  Qing-Long Han,et al.  State Estimation for Static Neural Networks With Time-Varying Delays Based on an Improved Reciprocally Convex Inequality , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Xuyang Lou,et al.  Delay-Dependent Criteria for Global Robust Periodicity of Uncertain Switched Recurrent Neural Networks With Time-Varying Delay , 2008, IEEE Transactions on Neural Networks.

[20]  Jian Yu,et al.  Triple-integral method for the stability analysis of delayed neural networks , 2013, Neurocomputing.

[21]  Peng Shi,et al.  Stability of switched positive linear systems with average dwell time switching , 2012, Autom..

[22]  Wei Xing Zheng,et al.  Exponential Stability Analysis for Delayed Neural Networks With Switching Parameters: Average Dwell Time Approach , 2010, IEEE Transactions on Neural Networks.

[23]  Juing-Shian Chiou,et al.  Stability and stabilization of Takagi–Sugeno fuzzy switched system with time-delay , 2012, J. Syst. Control. Eng..

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

[25]  Xian Zhang,et al.  DELAY-RANGE-DEPENDENT ROBUST H1 FILTERING FOR SINGULAR LPV SYSTEMS WITH TIME VARIANT DELAY , 2013 .

[26]  Junmin Wang,et al.  $\mathcal{H}_{\infty}$ Observer Design for LPV Systems With Uncertain Measurements on Scheduling Variables: Application to an Electric Ground Vehicle , 2016, IEEE/ASME Transactions on Mechatronics.

[27]  Hamid Reza Karimi,et al.  Dissipativity-Based Fuzzy Integral Sliding Mode Control of Continuous-Time T-S Fuzzy Systems , 2018, IEEE Transactions on Fuzzy Systems.

[28]  Amin Ramezanifar,et al.  A new method of parameter-varying filter design for LPV systems with time-varying state delay , 2015, 2015 American Control Conference (ACC).

[29]  Jiuwen Cao.  Improved Delay-Dependent Stability Conditions for MIMO Networked Control Systems with Nonlinear Perturbations , 2014, TheScientificWorldJournal.

[30]  Ju H. Park,et al.  Stability for Neural Networks With Time-Varying Delays via Some New Approaches , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[31]  James Lam,et al.  Weighted H∞ Filtering of Switched Systems with Time-Varying Delay: Average Dwell Time Approach , 2009, Circuits Syst. Signal Process..

[32]  Lixian Zhang,et al.  STABILITY OF A CLASS OF SWITCHED LINEAR SYSTEMS WITH UNCERTAINTIES AND AVERAGE DWELL TIME SWITCHING , 2010 .

[33]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

[34]  Karolos M. Grigoriadis,et al.  LPV Systems with parameter-varying time delays: analysis and control , 2001, Autom..

[35]  Shengyuan Xu,et al.  Robust H ∞ filtering for uncertain discrete piecewise time-delay systems , 2007, Int. J. Control.

[36]  Magdi S. Mahmoud,et al.  Robust H∞ filtering for switched stochastic systems under asynchronous switching , 2012, J. Frankl. Inst..

[37]  Hamid Reza Karimi,et al.  Sliding Mode Control of Fuzzy Singularly Perturbed Systems With Application to Electric Circuit , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[38]  Peng Shi,et al.  Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time , 2009, IEEE Transactions on Automatic Control.

[39]  Peng Shi,et al.  $l_{2}-l_{\infty}$ Model Reduction for Switched LPV Systems With Average Dwell Time , 2008, IEEE Transactions on Automatic Control.

[40]  Lihong Huang,et al.  A new delay-dependent H∞ control criterion for a class of discrete-time systems with time-varying state delays and input delays , 2008 .

[41]  Wei Xing Zheng,et al.  HMM-Based $\mathcal{H}_{\infty}$ Filtering for Discrete-Time Markov Jump LPV Systems Over Unreliable Communication Channels , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[42]  Jun Wang,et al.  Passivity of Switched Recurrent Neural Networks With Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Huijun Gao,et al.  A Parameter-Dependent Approach to Robust $H_{\infty }$ Filtering for Time-Delay Systems , 2008, IEEE Transactions on Automatic Control.

[44]  Peng Shi,et al.  Delay-dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay , 2011, Neurocomputing.

[45]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[46]  Hamid Reza Karimi,et al.  Reliable Output Feedback Control of Discrete-Time Fuzzy Affine Systems With Actuator Faults , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.