Non-fragile H∞ control with randomly occurring gain variations

In this paper, the non-fragile H∞ control problem is investigated for a class of discrete-time systems with randomly occurring gain variations (ROGVs). ROGVs, which describe the new network-induced phenomenon of a controller gain appearing in a random way, are modeled by a Bernoulli distributed white sequence with a known conditional probability. We aim to analyze and design a non-fragile H∞ output-feedback controller such that the closed-loop control system is stochastically stable while the desired H∞ performance is guaranteed. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the stochastic stability as well as prescribed H∞ disturbance-rejection attenuation. The controller design issue is then casted into a convex optimization one solvable by the semi-definite programme method. The effectiveness of the proposed method is demonstrated in the numerical example.

[1]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[2]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[3]  Shankar P. Bhattacharyya,et al.  Robust, fragile or optimal? , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[4]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  Shlomo Shamai,et al.  Fading Channels: Information-Theoretic and Communication Aspects , 1998, IEEE Trans. Inf. Theory.

[6]  Joseph R. Corrado,et al.  Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations , 2000 .

[7]  Jianliang Wang,et al.  Non-fragile Hinfinity control for linear systems with multiplicative controller gain variations , 2001, Autom..

[8]  Emilia Fridman,et al.  Robust H∞ control of distributed delay systems with application to combustion control , 2001, IEEE Trans. Autom. Control..

[9]  R. Gallager,et al.  Communication over fading channels with delay constraints , 2002, IEEE Trans. Inf. Theory.

[10]  J. Lam,et al.  Non‐fragile guaranteed cost control for uncertain descriptor systems with time‐varying state and input delays , 2005 .

[11]  H. Shu,et al.  H∞ analysis of nonlinear stochastic time-delay systems , 2005 .

[12]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[13]  Sirish L. Shah,et al.  Optimal H2 filtering with random sensor delay, multiple packet dropout and uncertain observations , 2007, Int. J. Control.

[14]  C. Lien,et al.  Non-fragile observer-based controls of linear system via LMI approach , 2007 .

[15]  Tongwen Chen,et al.  Optimal ${\cal H}_{2}$ Filtering in Networked Control Systems With Multiple Packet Dropout , 2007, IEEE Transactions on Automatic Control.

[16]  Michael V. Basin,et al.  Itô–Volterra Optimal State Estimation With Continuous, Multirate, Randomly Sampled, and Delayed Measurements , 2007, IEEE Transactions on Automatic Control.

[17]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Lihua Xie,et al.  Optimal linear estimation for systems with multiple packet dropouts , 2008, Autom..

[19]  Peng Shi,et al.  Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems , 2009, J. Frankl. Inst..

[20]  Wenwu Yu,et al.  Distributed Consensus Filtering in Sensor Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Y. Jia,et al.  Non-fragile dynamic output feedback control for linear systems with time-varying delay , 2009 .

[22]  James Lam,et al.  Non-Fragile Exponential Stability Assignment of Discrete-Time Linear Systems With Missing Data in Actuators , 2009, IEEE Transactions on Automatic Control.

[23]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[24]  Richard M. Murray,et al.  To Drop or Not to Drop: Design Principles for Kalman Filtering Over Wireless Fading Channels , 2009, IEEE Transactions on Automatic Control.

[25]  Donghua Zhou,et al.  Robust fault detection for networked systems with communication delay and data missing , 2009, Autom..

[26]  Xingyu Wang,et al.  Output-feedback control design for NCSs subject to quantization and dropout , 2009, Inf. Sci..

[27]  Yurong Liu,et al.  A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances , 2010, Autom..

[28]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[29]  Yeung Sam Hung,et al.  Distributed H∞-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case , 2010, Autom..

[30]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[31]  Hui Zhang,et al.  Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems , 2011, IEEE Transactions on Industrial Electronics.

[32]  M. Benrejeb,et al.  New delay-dependent stability conditions for linear systems with delay , 2011, 2011 International Conference on Communications, Computing and Control Applications (CCCA).

[33]  Michael V. Basin,et al.  Central suboptimal mean-square H ∞ controller design for linear stochastic time-varying systems , 2011, Int. J. Syst. Sci..

[34]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[35]  Zidong Wang,et al.  $H_{\infty}$ State Estimation for Discrete-Time Complex Networks With Randomly Occurring Sensor Saturations and Randomly Varying Sensor Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[36]  Andrea J. Goldsmith,et al.  LQG Control for MIMO Systems Over Multiple Erasure Channels With Perfect Acknowledgment , 2012, IEEE Transactions on Automatic Control.

[37]  Daniel E. Quevedo,et al.  On Kalman filtering over fading wireless channels with controlled transmission powers , 2012, Autom..

[38]  Mourad Kchaou,et al.  A new approach to non-fragile H ∞ observer-based control for discrete-time fuzzy systems , 2012, Int. J. Syst. Sci..

[39]  Ju H. Park,et al.  Non-fragile synchronization of neural networks with time-varying delay and randomly occurring controller gain fluctuation , 2013, Appl. Math. Comput..

[40]  Ligang Wu,et al.  Nonfragile Output Tracking Control of Hypersonic Air-Breathing Vehicles With an LPV Model , 2013, IEEE/ASME Transactions on Mechatronics.

[41]  Yonggui Kao,et al.  Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates , 2014, IEEE Transactions on Automatic Control.

[42]  Jinling Liang,et al.  Finite-horizon H∞ filtering for time-varying delay systems with randomly varying nonlinearities and sensor saturations , 2014 .