On stabilization of switching linear systems

This paper addresses the problem of controlling a continuous-time linear system that may switch among different modes taken from a finite set. The current mode of the system is supposed to be unknown. Moreover, unknown but bounded disturbances are assumed to affect the dynamics as well as the measurements. The proposed methodology is based on a minimum-distance mode estimator which orchestrates controller switching according to a dwell-time switching logic. Provided that the controllers are designed so as to ensure a certain mode observability condition and that the plant switching signal is slow on the average, the resulting control system turns out to be exponentially input-to-state stable.

[1]  Giorgio Battistelli,et al.  Stabilization and tracking for switching linear systems under unknown switching sequences , 2013, Syst. Control. Lett..

[2]  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).

[3]  Zvi Artstein,et al.  On stabilization of switched linear systems , 2008, Syst. Control. Lett..

[4]  Franco Blanchini,et al.  Nonquadratic Lyapunov functions for robust control , 1995, Autom..

[5]  A. Stephen Morse,et al.  Control Using Logic-Based Switching , 1997 .

[6]  Rafael Castro-Linares,et al.  Trajectory tracking for non-holonomic cars: A linear approach to controlled leader-follower formation , 2010, 49th IEEE Conference on Decision and Control (CDC).

[7]  Giorgio Battistelli,et al.  A maximum-likelihood Kalman filter for switching discrete-time linear systems , 2010, Autom..

[8]  João Pedro Hespanha,et al.  Postprints from CCDC Title Hysteresis-based switching algorithms for supervisory control of uncertain systems Permalink , 2002 .

[9]  Giorgio Battistelli,et al.  Multi-model unfalsified adaptive switching supervisory control , 2010, Autom..

[10]  Elena De Santis.  On location observability notions for switching systems , 2011, Syst. Control. Lett..

[11]  João Pedro Hespanha,et al.  Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle , 2004, IEEE Transactions on Automatic Control.

[12]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[13]  Giorgio Battistelli,et al.  Active mode observability of switching linear systems , 2007, Autom..

[14]  E. Davison,et al.  Properties of linear time-invariant multivariable systems subject to arbitrary output and state feedback , 1973 .

[15]  Maria Domenica Di Benedetto,et al.  A structural approach to detectability for a class of hybrid systems , 2009, Autom..

[16]  Z. G. Lia,et al.  Observer-based stabilization of switching linear systems , 2003 .

[17]  George J. Pappas,et al.  Observability of Switched Linear Systems in Continuous Time , 2005, HSCC.

[18]  S. Shankar Sastry,et al.  Observability of Linear Hybrid Systems , 2003, HSCC.

[19]  Y. Wu,et al.  Stabilisability of switched linear systems with time-varying delay in the detection of switching signals , 2009 .

[20]  Giorgio Battistelli,et al.  Maximum-likelihood Kalman filtering for switching discrete-time linear systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[21]  João Pedro Hespanha,et al.  Switching between stabilizing controllers , 2002, Autom..

[22]  Elena De Santis,et al.  Observer‐based stabilization of linear switching systems , 2009 .

[23]  Ji-Woong Lee,et al.  Uniform stabilization of discrete-time switched and Markovian jump linear systems , 2006, Autom..

[24]  M. Vidyasagar,et al.  A note on the genericity of simultaneous stabilizability and pole assignability , 1986 .

[25]  Giorgio Battistelli,et al.  Active mode observation of switching systems based on set‐valued estimation of the continuous state , 2009 .

[26]  Daniel E. Miller,et al.  Step Tracking in the Presence of Persistent Plant Changes , 2011, IEEE Transactions on Automatic Control.

[27]  Franco Blanchini,et al.  A Separation Principle for Linear Switching Systems and Parametrization of All Stabilizing Controllers , 2008, IEEE Transactions on Automatic Control.

[28]  Giorgio Battistelli,et al.  Receding-horizon estimation for switching discrete-time linear systems , 2005, IEEE Transactions on Automatic Control.

[29]  Maria Domenica Di Benedetto,et al.  Discrete state observability of hybrid systems , 2009 .

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

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