Disturbance attenuation and rejection for discrete-time Markovian jump systems with lossy measurements

Abstract This study addresses the disturbance attenuation and rejection problem for discrete-time Markovian jump systems with lossy measurements and multiple disturbances. The measurements transmitted from the plant to the observer and the controller are assumed to be imperfect, and two stochastic variables are utilized to model the missing data separately. A composite disturbance observer-based control and H ∞ control scheme is proposed for attenuating and rejecting the disturbances. This method is focused on the design of a new structure for the disturbance observer, dynamic output feedback controller, and composite controller, such that the composite system is stochastically stable and it satisfies scheduled performance requirements. The computation-oriented conditions of the disturbance observer gains and controller matrices for the controlled plant are provided based on the piecewise quadratic Lyapunov functional approach. Finally, a numerical example is provided to demonstrate the utility and applicability of the proposed theoretical method.

[1]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[2]  Yuguang Fang,et al.  Stabilization of continuous-time jump linear systems , 2002, IEEE Trans. Autom. Control..

[3]  Ole Morten Aamo,et al.  Disturbance rejection in 2 x 2 linear hyperbolic systems , 2013, IEEE Transactions on Automatic Control.

[4]  Ligang Wu,et al.  Output Feedback Control of Markovian Jump Repeated Scalar Nonlinear Systems , 2014 .

[5]  M. Branicky.  Stability of switched and hybrid systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  Riccardo Marino,et al.  Global compensation of unknown sinusoidal disturbances for a class of nonlinear nonminimum phase systems , 2005, IEEE Transactions on Automatic Control.

[7]  Toshio Fukuda,et al.  A nonlinear disturbance observer for multivariable systems and its application to magnetic bearing systems , 2004, IEEE Transactions on Control Systems Technology.

[8]  Lei Guo,et al.  Hierarchical anti-disturbance adaptive control for non-linear systems with composite disturbances and applications to missile systems , 2011 .

[9]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[10]  Lei Guo,et al.  Stochastic Distribution Control System Design: A Convex Optimization Approach , 2010 .

[11]  V. O. Nikiforov,et al.  Nonlinear servocompensation of unknown external disturbances , 2001, Autom..

[12]  Ken Chen,et al.  Frequency-Domain Analysis of Nonlinear Active Disturbance Rejection Control via the Describing Function Method , 2013, IEEE Transactions on Industrial Electronics.

[13]  Yasuhiro Ohyama,et al.  A new approach to the estimation and rejection of disturbances in servo systems , 2005, IEEE Transactions on Control Systems Technology.

[14]  Robert R. Bitmead,et al.  Rejection of Aliased Disturbances in a Production Pulsed Light Source , 2013, IEEE Transactions on Control Systems Technology.

[15]  Wen-Hua Chen,et al.  Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach , 2005 .

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

[17]  Lei Guo,et al.  Composite disturbance‐observer‐based control and H∞ control for complex continuous models , 2010 .

[18]  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.

[19]  Wen-an Zhang,et al.  Hinfinity filtering of networked discrete-time systems with random packet losses , 2009, Inf. Sci..

[20]  A. Isidori.  Nonlinear Control Systems , 1985 .

[21]  Meng Li,et al.  CONSENSUS PROBLEMS FOR HIGH-ORDER LTI SYSTEMS: A DECENTRALIZED STATIC OUTPUT FEEDBACK METHOD , 2013 .

[22]  El-Kébir Boukas,et al.  Stochastic Switching Systems: Analysis and Design , 2005 .

[23]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[24]  Wen-Hua Chen,et al.  Disturbance observer based control for nonlinear systems , 2004 .

[25]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[26]  Peng Shi,et al.  Robust quantized H∞ control for network control systems with Markovian jumps and time delays , 2013 .

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

[28]  Xinjiang Wei,et al.  Composite disturbance-observer-based control and variable structure control for non-linear systems with disturbances , 2009 .

[29]  Raja Sengupta,et al.  A bounded real lemma for jump systems , 2003, IEEE Trans. Autom. Control..

[30]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[31]  Ligang Wu,et al.  Sensor Networks With Random Link Failures: Distributed Filtering for T–S Fuzzy Systems , 2013, IEEE Transactions on Industrial Informatics.

[32]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[33]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[34]  E. Davison.  The robust control of a servomechanism problem for linear time-invariant multivariable systems , 1976 .

[35]  Konrad Reif,et al.  Stochastic Stability of the Extended Kalman Filter With Intermittent Observations , 2010, IEEE Transactions on Automatic Control.

[36]  Michel Verhaegen,et al.  Rejection of Periodic Wind Disturbances on a Smart Rotor Test Section Using Lifted Repetitive Control , 2013, IEEE Transactions on Control Systems Technology.