Generalized switching signals for input-to-state stability of switched systems

This article deals with input-to-state stability (ISS) of continuous-time switched nonlinear systems. Given a family of systems with exogenous inputs such that not all systems in the family are ISS, we characterize a new and general class of switching signals under which the resulting switched system is ISS. Our stabilizing switching signals allow the number of switches to grow faster than an affine function of the length of a time interval, unlike in the case of average dwell time switching. We also recast a subclass of average dwell time switching signals in our setting and establish analogs of two representative prior results.

[1]  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).

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

[3]  Debasish Chatterjee,et al.  Stabilizing discrete-time switched systems with inputs , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[4]  W. J. Kaczor,et al.  Real numbers, sequences and series , 2000 .

[5]  Debasish Chatterjee,et al.  Stabilizing Switching Signals for Switched Systems , 2015, IEEE Transactions on Automatic Control.

[6]  A. Morse.  Supervisory control of families of linear set-point controllers , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[7]  Piotr Biler,et al.  Problems in mathematical analysis , 1990 .

[8]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[9]  A. Morse.  Supervisory control of families of linear set-point controllers. 2. Robustness , 1997, IEEE Trans. Autom. Control..

[10]  Guosong Yang,et al.  Input-to-state stability for switched systems with unstable subsystems: A hybrid Lyapunov construction , 2014, 53rd IEEE Conference on Decision and Control.

[11]  Daniel Liberzon,et al.  Input/output-to-state stability and state-norm estimators for switched nonlinear systems , 2012, Autom..

[12]  A. Morse.  Supervisory control of families of linear set-point controllers Part I. Exact matching , 1996, IEEE Trans. Autom. Control..

[13]  Zhengguo Li,et al.  Input-to-state stabilization of switched nonlinear systems , 2001, IEEE Trans. Autom. Control..

[14]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[15]  A. Stephen Morse,et al.  Switched nonlinear systems with state-dependent dwell-time , 2003, Syst. Control. Lett..

[16]  Debasish Chatterjee,et al.  Input-to-state stability of switched systems and switching adaptive control , 2007, Autom..

[17]  Eduardo Sontag,et al.  Forward Completeness, Unboundedness Observability, and their Lyapunov Characterizations , 1999 .

[18]  Eduardo D. Sontag,et al.  Input-Output-to-State Stability , 2001, SIAM J. Control. Optim..

[19]  W. J. Kaczor,et al.  Problems in mathematical analysis , 2000 .