Uniform stability properties of switched systems with switchings governed by digraphs

Characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph, are developed. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions.

[1]  Eduardo D. Sontag,et al.  On the representation of switched systems with inputs by perturbed control systems , 2005 .

[2]  Karl Henrik Johansson,et al.  Dynamical properties of hybrid automata , 2003, IEEE Trans. Autom. Control..

[3]  J. L. Mancilla-Aguilar,et al.  A converse Lyapunov theorem for nonlinear switched systems , 2000 .

[5]  David Angeli,et al.  Uniform Global Asymptotic Stability of Differential Inclusions , 2004 .

[6]  J. L. Mancilla-Aguilar,et al.  On converse Lyapunov theorems for ISS and iISS switched nonlinear systems , 2001 .

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

[8]  Eduardo D. Sontag,et al.  Measurement to error stability: a notion of partial detectability for nonlinear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  David Angeli,et al.  Separation Principles for Input-Output and Integral-Input-to-State Stability , 2004, SIAM J. Control. Optim..

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

[11]  Eduardo D. Sontag,et al.  Lyapunov Characterizations of Input to Output Stability , 2000, SIAM J. Control. Optim..

[12]  J. L. Mancilla-Aguilar,et al.  State-norm estimation of switched nonlinear systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[13]  Dieter Jungnickel,et al.  Graphs, Networks, and Algorithms , 1980 .

[14]  Eduardo Sontag,et al.  Notions of input to output stability , 1999, Systems & Control Letters.

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