Passivity analysis and control for discrete-time two-dimensional switched systems in Roesser model

ABSTRACT This paper investigates the passivity issues of discrete-time two-dimensional switched systems in Roesser model under a state-dependent switching law. Conditions for passivity of discrete-time two-dimensional switched systems are obtained without the requirement of passivity of subsystems. When the system states are completely available, state feedback controllers and switching laws are designed. In the case of partial state measurements, dynamic output feedback controllers and switching laws depending only on the state of the output feedback controllers are constructed to guarantee passivity of the closed-loop switched system. Finally, numerical examples are provided to illustrate the efficiency of the results.

[1]  Patrizio Colaneri,et al.  Passivity of switched linear systems: Analysis and control design , 2012, Syst. Control. Lett..

[2]  Cishen Zhang,et al.  H2 and mixed H2/Hinfinity control of two-dimensional systems in Roesser model , 2006, Autom..

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

[4]  Cishen Zhang,et al.  Hinfinity control and robust stabilization of two-dimensional systems in Roesser models , 2001, Autom..

[5]  Alberto Bemporad,et al.  Passivity Analysis and Passification of Discrete-Time Hybrid Systems , 2008, IEEE Transactions on Automatic Control.

[6]  Robert Cimochowski.  Asymptotic stability of the positive switched 2D linear systems described by the Roesser models , 2011, 2011 16th International Conference on Methods & Models in Automation & Robotics.

[7]  Hamid Reza Karimi,et al.  Delay-dependent exponential stabilization of positive 2D switched state-delayed systems in the Roesser model , 2014, Inf. Sci..

[8]  Junping Du,et al.  Robust Consensus Tracking Control for Multiagent Systems With Initial State Shifts, Disturbances, and Switching Topologies , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[9]  K. Narendra,et al.  A common Lyapunov function for stable LTI systems with commuting A-matrices , 1994, IEEE Trans. Autom. Control..

[10]  Peng Shi,et al.  Two-Dimensional Dissipative Control and Filtering for Roesser Model , 2015, IEEE Transactions on Automatic Control.

[11]  Zhengrong Xiang,et al.  Output Feedback H∞ Stabilization of 2D Discrete Switched Systems in FM LSS Model , 2014, Circuits Syst. Signal Process..

[12]  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..

[13]  B. Brogliato,et al.  Dissipative Systems Analysis and Control , 2000 .

[14]  M. Zefran,et al.  A notion of passivity for hybrid systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[16]  P.J. Antsaklis,et al.  Switching Stabilization and l2 Gain Performance Controller Synthesis for Discrete-Time Switched Linear Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[17]  M. Mahmoud,et al.  Passivity and passification of time-delay systems , 2004 .

[18]  Mikhail A. Emelianov,et al.  Dissipativity of Nonlinear 2D Systems , 2015 .

[19]  Peng Shi,et al.  Modeling and adaptive tracking for a class of stochastic Lagrangian control systems , 2013, Autom..

[20]  Ligang Wu,et al.  Stability analysis for discrete-time two-dimensional switched systems , 2015, 2015 34th Chinese Control Conference (CCC).

[21]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[22]  Lihua Xie,et al.  H∞ filtering of 2-D discrete systems , 2000, IEEE Trans. Signal Process..

[23]  Zhengrong Xiang,et al.  Design of an Iterative Learning Control Law for a Class of Switched Repetitive Systems , 2017, Circuits Syst. Signal Process..

[24]  Zhengrong Xiang,et al.  H∞ control of a class of 2-D continuous switched delayed systems via state-dependent switching , 2016, Int. J. Syst. Sci..

[25]  Krzysztof Galkowski,et al.  Dissipativity and stabilization of nonlinear repetitive processes , 2016, Syst. Control. Lett..

[26]  M. Jirstrand,et al.  On stability and passivity of a class of hybrid systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[27]  K. Hu,et al.  Improved robust H8 filtering for uncertain discrete-time switched systems , 2009 .

[28]  Ju H. Park,et al.  Novel results on robust finite-time passivity for discrete-time delayed neural networks , 2016, Neurocomputing.

[29]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[30]  Guang-Hong Yang,et al.  Passivity and output feedback passification of switched continuous-time systems with a dwell time constraint , 2015 .

[31]  M. Morari,et al.  Stability and stabilization of piecewise affine and hybrid systems: an LMI approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[32]  James Lam,et al.  Stability and Dissipativity Analysis of Distributed Delay Cellular Neural Networks , 2011, IEEE Transactions on Neural Networks.

[33]  Lihua Xie,et al.  Dissipative control for linear discrete-time systems , 1999, Autom..

[34]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[35]  Z. Xiang,et al.  Robust reliable control of uncertain 2D discrete switched systems with state delays , 2012, 1206.5508.

[36]  Mehrdad Saif,et al.  PASSIVITY AND PASSIVITY BASED CONTROLLER DESIGN OF A CLASS OF SWITCHED CONTROL SYSTEMS , 2005 .

[37]  Shengyuan Xu,et al.  Robust stability and stabilisation of 2D discrete state-delayed systems , 2004, Syst. Control. Lett..

[38]  T. Hinamoto.  Stability of 2-D discrete systems described by the Fornasini-Marchesini second model , 1997 .

[39]  Vimal Singh,et al.  An improved criterion for the asymptotic stability of 2-D digital filters described by the Fornasini-Marchesini second model using saturation arithmetic , 1999 .

[40]  Krzysztof Galkowski,et al.  Stabilization of nonlinear 2D Fornasini-Marchesini and Roesser systems , 2015, 2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS).

[41]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[42]  Zhengrong Xiang,et al.  Stability Analysis and Stabilization of Discrete-Time 2D Switched Systems , 2012, Circuits, Systems, and Signal Processing.

[43]  Lihua Xie,et al.  H[∞] control and filtering of two-dimensional systems , 2002 .

[44]  Jun Zhao,et al.  Dissipativity Theory for Switched Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[45]  F. M. Callier,et al.  Dissipative Systems Analysis and Control: Theory and Applications (2nd Edition)-[Book review; B. Brogliato, R. Lozano, B. Maschke] , 2007, IEEE Transactions on Automatic Control.