Resilient Dissipative Filtering for Uncertain Markov Jump Nonlinear Systems with Time-Varying Delays

The resilient dissipative filtering problem for a class of uncertain time-delay Markov jump nonlinear systems is studied in this paper. The nonlinear functions are assumed to belong to sector sets with arbitrary boundaries. The sector boundaries can have positive and/or negative slopes, and therefore, we cover the most general case in our approach. Using the special structure of the system, and by constructing a new multiple Lyapunov–Krasovskii function, the sufficient conditions regarding the existence of desired resilient dissipative filters are obtained in terms of linear matrix inequalities, which ensure the filtering error system is stochastically stable and strictly dissipative. The designed filter can tolerate additive uncertainties in the filter gain matrix, which results from filter implementations. A numerical example is presented to show the effectiveness of the proposed theoretical results.

[1]  Yuxin Zhao,et al.  Resilient Asynchronous $H_{\infty }$ Filtering for Markov Jump Neural Networks With Unideal Measurements and Multiplicative Noises , 2015, IEEE Transactions on Cybernetics.

[2]  Chaoxu Guan,et al.  Improved H∞ filter design for discrete-time Markovian jump systems with time-varying delay , 2016, J. Frankl. Inst..

[3]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[4]  J. Willems Dissipative dynamical systems part I: General theory , 1972 .

[5]  Junfeng Chen,et al.  Robust delay-range-dependent non-fragile H∞ filtering for uncertain neutral stochastic systems with Markovian switching and mode-dependent time delays , 2015, J. Frankl. Inst..

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

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

[8]  Bart De Schutter,et al.  Stabilization and robust H⃵ control for sector-bounded switched nonlinear systems , 2014, Autom..

[9]  Wei Yang,et al.  Non-fragile strictly dissipative filter for discrete-time nonlinear systems with sector-bounded nonlinearities , 2010, 2010 Chinese Control and Decision Conference.

[10]  Magdi S. Mahmoud,et al.  Resilient linear filtering of uncertain systems , 2004, Autom..

[11]  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.

[12]  R. P. Marques,et al.  Discrete-Time Markov Jump Linear Systems , 2004, IEEE Transactions on Automatic Control.

[13]  Jiujun Cheng,et al.  Robust H∞ Filtering for Uncertain Nonlinear Stochastic Systems with Mode-dependent Time-delays and Markovian Jump Parameters , 2011, Circuits Syst. Signal Process..

[14]  G. Song,et al.  Stability and l 2 -gain analysis for a class of discrete-time non-linear Markovian jump systems with actuator saturation and incomplete knowledge of transition probabilities , 2012 .

[15]  Hao Shen,et al.  Extended passive filtering for discrete-time singular Markov jump systems with time-varying delays , 2016, Signal Process..

[16]  James Lam,et al.  Robust reliable dissipative filtering for discrete delay singular systems , 2012, Signal Process..

[17]  Huijun Gao,et al.  Adaptive Robust Vibration Control of Full-Car Active Suspensions With Electrohydraulic Actuators , 2013, IEEE Transactions on Control Systems Technology.

[18]  Huijun Gao,et al.  Vibration Isolation for Active Suspensions With Performance Constraints and Actuator Saturation , 2015, IEEE/ASME Transactions on Mechatronics.

[19]  Rathinasamy Sakthivel,et al.  Robust reliable dissipative filtering for Markovian jump nonlinear systems with uncertainties , 2017 .

[20]  Yunliang Wei,et al.  Non-Fragile $$H_{\infty }$$H∞ Filter Design for Uncertain Stochastic Nonlinear Time-Delay Markovian Jump Systems , 2014, Circuits Syst. Signal Process..

[21]  Oswaldo Luiz V. Costa,et al.  Robust mode-independent filtering for discrete-time Markov jump linear systems with multiplicative noises , 2013, Int. J. Control.

[22]  Peng Shi,et al.  Dissipativity Analysis for Discrete-Time Stochastic Neural Networks With Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Liu Fei,et al.  Exponential passive filtering for a class of nonlinear jump systems , 2012 .

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

[25]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.

[26]  J.C. Geromel,et al.  ${\cal H}_{\infty}$ Filtering of Discrete-Time Markov Jump Linear Systems Through Linear Matrix Inequalities , 2009, IEEE Transactions on Automatic Control.

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

[28]  Oswaldo Luiz V. Costa,et al.  Stochastic stabilization and induced l2-gain for discrete-time Markov jump Lur'e systems with control saturation , 2014, Autom..

[29]  Wei Xing Zheng,et al.  Distributed ℋ∞ Filtering for a Class of Discrete-Time Markov Jump Lur'e Systems With Redundant Channels , 2016, IEEE Trans. Ind. Electron..

[30]  Huijun Gao,et al.  Finite Frequency $H_{\infty }$ Control for Vehicle Active Suspension Systems , 2011, IEEE Transactions on Control Systems Technology.

[31]  Yimin Zhou,et al.  Observer-based l2-l∞ control for discrete-time nonhomogeneous Markov jump Lur'e systems with sensor saturations , 2015, Neurocomputing.

[32]  Huijun Gao,et al.  Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties , 2006 .

[33]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[34]  Wei Xing Zheng,et al.  Energy-to-Peak State Estimation for Markov Jump RNNs With Time-Varying Delays via Nonsynchronous Filter With Nonstationary Mode Transitions , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Ju H. Park,et al.  Robust mixed H∞ and passive filtering for networked Markov jump systems with impulses , 2014, Signal Process..

[36]  Yi-Fu Feng,et al.  Dissipative filtering for linear discrete-time systems via LMI , 2009, 2009 Chinese Control and Decision Conference.

[37]  D. E. Brown,et al.  Theory of Markov Processes. , 1962 .