Controllability and observability of switched linear systems with continuous-time and discrete-time subsystems [Brief Paper]

In this study, the authors focus on the controllability and observability of switched linear systems composed by continuous-time and discrete-time subsystems. Necessary and sufficient conditions for controllability and observability are obtained. A simple example is proposed to illustrate the effectiveness of the current theoretical results.

[1]  Guangming Xie,et al.  Reachability realization and stabilizability of switched linear discrete-time systems☆ , 2003 .

[2]  A. Willsky,et al.  Discrete-time Markovian-jump linear quadratic optimal control , 1986 .

[3]  Shuzhi Sam Ge,et al.  Controllability and reachability criteria for switched linear systems , 2002, Autom..

[4]  Shuzhi Sam Ge,et al.  Reachability and controllability of switched linear discrete-time systems , 2001, IEEE Trans. Autom. Control..

[5]  Jitao Sun,et al.  Controllability and observability for impulsive systems in complex fields , 2010 .

[6]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[7]  David P. Stanford,et al.  Stability for a Multi-Rate Sampled-Data System , 1979 .

[8]  Antonio Ramírez-Treviño,et al.  Observability of Switched Linear Systems , 2010, IEEE Transactions on Industrial Informatics.

[9]  Kumpati S. Narendra,et al.  Adaptive control using multiple models , 1997, IEEE Trans. Autom. Control..

[10]  Enrique A. Medina,et al.  Reachability and observability of linear impulsive systems , 2008, Autom..

[11]  Luther Conner,et al.  State deadbeat response and observability in multi-modal systems , 1983, The 22nd IEEE Conference on Decision and Control.

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

[13]  Jitao Sun,et al.  A geometric approach for reachability and observability of linear switched impulsive systems , 2010 .

[14]  Zhendong Sun Reachability analysis of constrained switched linear systems , 2007, Autom..

[15]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

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

[17]  W. Brogan Modern Control Theory , 1971 .

[18]  I. Kolmanovsky,et al.  Hybrid feedback laws for a class of cascade nonlinear control systems , 1996, IEEE Trans. Autom. Control..

[19]  Roger W. Brockett,et al.  Electrical networks containing controlled switches , 1974 .

[20]  Zhenyu Yang,et al.  An algebraic approach towards the controllability of controlled switching linear hybrid systems , 2002, Autom..

[21]  Horacio J. Marquez,et al.  Controllability and Observability for a Class of Controlled Switching Impulsive Systems , 2008, IEEE Transactions on Automatic Control.

[22]  Guangming Xie,et al.  Necessary and sufficient conditions for controllability and observability of switched impulsive control systems , 2004, IEEE Transactions on Automatic Control.

[23]  Shuzhi Sam Ge,et al.  Switched Linear Systems , 2005 .

[24]  Jiang Xing,et al.  Controllability of switched systems with continuous-time and discrete-time subsystems , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[25]  Derong Liu,et al.  Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems , 2006, IEEE Trans. Circuits Syst. II Express Briefs.

[26]  Enrique A. Medina Linear Impulsive Control Systems: A Geometric Approach , 2007 .

[27]  D.D. Sworder,et al.  Control of systems subject to sudden change in character , 1976, Proceedings of the IEEE.

[28]  Hai Lin,et al.  Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Alexander Leonessa,et al.  Nonlinear system stabilization via hierarchical switching control , 2001, IEEE Trans. Autom. Control..

[30]  Long Wang,et al.  On Controllability of Switched Linear Systems , 2002, IEEE Transactions on Automatic Control.

[31]  Dan Zhao,et al.  Robust static output feedback design for polynomial nonlinear systems , 2010 .