Dwell time estimation algorithm for switched affine linear systems

This document shows a dwell time-based switching technique for affine linear systems. The affine system is defined as a parameter dependent homotopic combination of two base modes, where the intermediate modes create an “artificial” grid of subsystems, producing lower dwell times estimates, specially when the number of modes increases. In some practical applications, the interpolated modes may replace previously designed or existing modes over a defined variable or range. Finsler's lemma is used to develop a relaxed Lyapunov-based condition that ensures the stability of the switched system and reduces the computation time of the developed technique. A user-defined parameter is used to influence the dwell time estimation. Numerical calculations performed over a switched system derived from an adaptive vibration attenuation controller shows the effectiveness of the proposed algorithm.

[1]  Alexandre Trofino,et al.  Stabilizing switching rule design for affine switched systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[2]  G Chesi,et al.  Computing upper-bounds of the minimum dwell time of linear switched systems via homogeneous polynomial Lyapunov functions , 2010, Proceedings of the 2010 American Control Conference.

[3]  Mikael Johansson,et al.  Piecewise linear control systems - a computational approach , 2002, Lecture notes in control and information sciences.

[4]  Corentin Briat.  Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints , 2013, Autom..

[5]  Hai Lin,et al.  Stabilization and performance analysis for a class of switched systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[6]  Neslihan Serap Sengör,et al.  A dwell time approach to the stability of switched linear systems based on the distance between eigenvector sets , 2009, Int. J. Syst. Sci..

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

[8]  Corentin Briat,et al.  Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time , 2015, Syst. Control. Lett..

[9]  Patrizio Colaneri,et al.  A Nonconservative LMI Condition for Stability of Switched Systems With Guaranteed Dwell Time , 2012, IEEE Transactions on Automatic Control.

[10]  David Angeli,et al.  Nonlinear norm-observability notions and stability of switched systems , 2005, IEEE Transactions on Automatic Control.

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

[12]  Matthew C. Turner,et al.  Improved computation of dwell time using the real Jordan form , 2016, 2016 American Control Conference (ACC).

[13]  A. Morse,et al.  Stability of switched systems: a Lie-algebraic condition ( , 1999 .

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

[15]  V.F. Montagner,et al.  State feedback gain scheduling for linear systems with time-varying parameters , 2004, Proceedings of the 2004 American Control Conference.

[16]  A. Michel,et al.  PIECEWISE LYAPUNOV FUNCTIONS FOR SWITCHED SYSTEMS WITH AVERAGE DWELL TIME , 2000 .

[17]  Jakob Stoustrup,et al.  A parameterization of observer-ased controllers: Bumpless transfer by covariance interpolation , 2009, 2009 American Control Conference.

[18]  Matthew C. Turner,et al.  On the computation of dwell time using the real Jordan form , 2015, 2015 American Control Conference (ACC).

[19]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[20]  Joao P. Hespanha,et al.  Stabilization Through Hybrid Control , 2011 .

[21]  Michael Margaliot,et al.  Stability analysis of switched systems using variational principles: An introduction , 2006, Autom..

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

[23]  Alexandre Trofino,et al.  Switching rule design for affine switched systems using a max-type composition rule , 2014, Syst. Control. Lett..

[24]  Pedro L. D. Peres,et al.  A new LMI condition for the robust stability of linear time-varying systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[25]  Patrizio Colaneri,et al.  Stability and Stabilization of Continuous-Time Switched Linear Systems , 2006, SIAM J. Control. Optim..

[26]  Harald Pfifer,et al.  Generation of LPV models and LFRs for a Nonlinear Aircraft Model , 2012 .

[27]  Owen G. Thorp,et al.  Experimental verification of an optical beam stabilizing controller , 2012, 2012 American Control Conference (ACC).

[28]  Richard T. O'Brien,et al.  Adaptive H∞ Vibration Control , 2011 .

[29]  Alexandre Trofino,et al.  Switching Rule Design for Affine Switched Systems With Guaranteed Cost and Uncertain Equilibrium Condition , 2016, IEEE Transactions on Automatic Control.