Trajectory-based small gain theorems for ISpS and ISS of large-scale networks of switched systems with arbitrary switchings

The authors consider a large-scale switched non-linear system which is composed as an interconnection of N non-linear switched systems. Having assumed that every subsystem is stable uniformly with respect to the unobservable switching signals, it can happen that the entire interconnection is unstable. This study provides a sufficient condition for the uniform stability of the entire large-scale interconnection. The framework of input-to-state stability (ISS) is used for this purpose and the stability condition is of the small-gain type which is given in terms of trajectory-based ISS gains. To prove this result we extend the well-known result by Sontag and Wang on characterisations of the ISS property in terms of simpler stability notions to the case of switched systems with arbitrary switchings.

[1]  Eduardo Sontag,et al.  New characterizations of input-to-state stability , 1996, IEEE Trans. Autom. Control..

[2]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[3]  Ilia G. Polushin,et al.  Attitude Synchronization of Multiple Rigid Bodies With Communication Delays , 2012, IEEE Transactions on Automatic Control.

[4]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[5]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[6]  Fabian R. Wirth,et al.  An ISS small gain theorem for general networks , 2007, Math. Control. Signals Syst..

[7]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[8]  Zhong-Ping Jiang,et al.  Uniform asymptotic stabilization of nonlinear switched systems with arbitrary switchings and with dynamic uncertainties by means of small gain theorems , 2013, 52nd IEEE Conference on Decision and Control.

[9]  Jun Zhao,et al.  A Small-Gain Theorem for Switched Interconnected Nonlinear Systems and Its Applications , 2014, IEEE Transactions on Automatic Control.

[10]  Hiroshi Ito,et al.  State-Dependent Scaling Problems and Stability of Interconnected iISS and ISS Systems , 2006, IEEE Transactions on Automatic Control.

[11]  Sergey Dashkovskiy,et al.  A new small gain theorem for large-scale networks of switched systems with arbitrary switchings , 2015, 2015 European Control Conference (ECC).

[12]  Fabian R. Wirth,et al.  Small gain theorems for large scale systems and construction of ISS Lyapunov functions , 2009, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[13]  Zhong-Ping Jiang,et al.  A small-gain control method for nonlinear cascaded systems with dynamic uncertainties , 1997, IEEE Trans. Autom. Control..

[14]  Zhong-Ping Jiang,et al.  Distributed Output-Feedback Control of Nonlinear Multi-Agent Systems , 2013, IEEE Transactions on Automatic Control.

[15]  Rajnikant V. Patel,et al.  A small gain framework for networked cooperative force-reflecting teleoperation , 2013, Autom..

[16]  Dragan Nesic,et al.  Lyapunov-Based Small-Gain Theorems for Hybrid Systems , 2014, IEEE Transactions on Automatic Control.

[17]  Jenq-Lang Wu,et al.  Stabilizing controllers design for switched nonlinear systems in strict-feedback form , 2009, Autom..

[18]  Zhong-Ping Jiang,et al.  A generalization of the nonlinear small-gain theorem for large-scale complex systems , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[19]  A. Teel.  A nonlinear small gain theorem for the analysis of control systems with saturation , 1996, IEEE Trans. Autom. Control..

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

[21]  Peter Xiaoping Liu,et al.  A Multichannel IOS Small Gain Theorem for Systems With Multiple Time-Varying Communication Delays , 2009, IEEE Transactions on Automatic Control.

[22]  Zhong-Ping Jiang,et al.  Small-gain theorem for a wide class of feedback systems with control applications , 2007, 2007 European Control Conference (ECC).

[23]  Iasson Karafyllis,et al.  ISS property for time-varying systems and application to partial-static feedback stabilization and asymptotic tracking , 1999, IEEE Trans. Autom. Control..