Stability analysis of a class of switched linear systems on non-uniform time domains

Abstract This paper deals with the stability analysis of a class of switched linear systems on non-uniform time domains. The considered class consists of a set of linear continuous-time and linear discrete-time subsystems. First, some conditions are derived to guarantee the exponential stability of this class of systems on time scales with bounded graininess function when the subsystems are exponentially stable. These results are extended when considering an unstable discrete time subsystem or an unstable continuous-time subsystem. Some examples illustrate these results.

[1]  Zbigniew Bartosiewicz,et al.  On stabilisability of nonlinear systems on time scales , 2013, Int. J. Control.

[2]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[3]  Fabian R. Wirth,et al.  A spectral characterization of exponential stability for linear time-invariant systems on time scales , 2003 .

[4]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[5]  John M. Davis,et al.  STABILITY OF SIMULTANEOUSLY TRIANGULARIZABLE SWITCHED SYSTEMS ON HYBRID DOMAINS , 2014 .

[6]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[7]  Do Duc Thuan,et al.  Stability radius of implicit dynamic equations with constant coefficients on time scales , 2011, Syst. Control. Lett..

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

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

[10]  Zhengguo Li,et al.  Analysis and design of impulsive control systems , 2001, IEEE Trans. Autom. Control..

[11]  A. Michel,et al.  Analysis and design of switched normal systems , 2006 .

[12]  Robert J. Marks,et al.  Stability of switched linear systems on non-uniform time domains , 2010, 2010 42nd Southeastern Symposium on System Theory (SSST).

[13]  Robert J. Marks,et al.  CONTROLLABILITY, OBSERVABILITY, REALIZABILITY, AND STABILITY OF DYNAMIC LINEAR SYSTEMS , 2009, 0901.3764.

[14]  Luc Gauthier.  Commutation des matrices et congruences d'ordre un , 1956 .

[15]  Stefano Di Gennaro,et al.  Self-triggered control for multi-agent systems with unknown non-linear inherent dynamics , 2014 .

[16]  A. Peterson,et al.  Advances in Dynamic Equations on Time Scales , 2012 .

[17]  Mandeep Singh,et al.  Existence of solutions for three-point BVPs arising in bridge design , 2014 .

[18]  J. J. Dacunha.  Stability for time varying linear dynamic systems on time scales , 2005 .

[20]  G. Guseinov.  Integration on time scales , 2003 .

[21]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[22]  Mohamed Djemai,et al.  Stability of switched linear systems on time scale , 2013, 3rd International Conference on Systems and Control.

[23]  Fabian R. Wirth,et al.  Stability radii for positive linear time-invariant systems on time scales , 2010, Syst. Control. Lett..

[24]  Stefano Di Gennaro,et al.  Self-triggered control for multi-agent systems under a directed switching graph , 2013, 52nd IEEE Conference on Decision and Control.

[25]  G. Zhai,et al.  Quadratic stabilizability of switched linear systems with polytopic uncertainties , 2003 .

[26]  Youssef N. Raffoul,et al.  Exponential stability of dynamic equations on time scales , 2005 .

[27]  John M. Davis,et al.  Switched linear systems on time scales with relaxed commutativity constraints , 2011, 2011 IEEE 43rd Southeastern Symposium on System Theory.

[28]  M. Rashford,et al.  Exponential Stability of Dynamic Equations on Time Scales , 2022 .