Improving the performance of linear systems by adding a hybrid loop: The output feedback case

In this paper, we extend the state feedback results of Prieur et al. (NOLCOS 2010) to the linear output feedback case, when the plant state is not available and is estimated via a Luenberger observer. We propose two techniques based on different reset maps and flow and jump sets, guaranteeing global practical asymptotic stability of the origin of the closed-loop system. The effectiveness of the solutions is illustrated on a simulation example where we show suitable reduction of the output overshoot.

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

[2]  Sophie Tarbouriech,et al.  Guaranteed stability for nonlinear systems by means of a hybrid loop , 2010 .

[3]  Gregory Stewart,et al.  Quadratic optimization for controller initialization in multivariable switching systems , 2010, Proceedings of the 2010 American Control Conference.

[4]  Wassim M. Haddad,et al.  Non-linear impulsive dynamical systems. Part II: Stability of feedback interconnections and optimality , 2001 .

[5]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[6]  Luca Zaccarian,et al.  Analytical and numerical Lyapunov functions for SISO linear control systems with first‐order reset elements , 2011 .

[7]  Christopher V. Hollot,et al.  Analysis of reset control systems consisting of a FORE and second-order loop , 2001 .

[8]  Christophe Prieur,et al.  Asymptotic Controllability and Robust Asymptotic Stabilizability , 2001, SIAM J. Control. Optim..

[9]  João Pedro Hespanha,et al.  Stabilization of nonholonomic integrators via logic-based switching , 1999, Autom..

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

[11]  Luca Zaccarian,et al.  Stability and Performance of SISO Control Systems With First-Order Reset Elements , 2011, IEEE Transactions on Automatic Control.

[12]  Jean-Pierre Aubin,et al.  Impulse differential inclusions: a viability approach to hybrid systems , 2002, IEEE Trans. Autom. Control..

[13]  Sophie Tarbouriech,et al.  Stability analysis for reset systems with input saturation , 2007, 2007 46th IEEE Conference on Decision and Control.

[14]  Rafal Goebel,et al.  Hybrid Feedback Control and Robust Stabilization of Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[15]  W. P. M. H. Heemels,et al.  H2 performance analysis of reset control systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[16]  Sophie Tarbouriech,et al.  Improving the performance of linear systems by adding a hybrid loop , 2011 .

[17]  Ricardo G. Sanfelice,et al.  Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability , 2007, IEEE Transactions on Automatic Control.

[18]  K. C. Wong,et al.  Plant With Integrator: An Example of Reset Control Overcoming Limitations of Linear Feedback , 2001 .

[19]  Rafal Goebel,et al.  Solutions to hybrid inclusions via set and graphical convergence with stability theory applications , 2006, Autom..

[20]  C. Hollot,et al.  FUNDAMENTAL PROPERTIES OF RESET CONTROL SYSTEMS , 2002 .

[21]  Luca Zaccarian,et al.  Lazy sensors for the scheduling of measurement samples transmission in linear closed loops over networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[22]  L. Zaccarian,et al.  First order reset elements and the Clegg integrator revisited , 2005, Proceedings of the 2005, American Control Conference, 2005..

[23]  M Maarten Steinbuch,et al.  Performance analysis of reset control systems , 2010 .

[24]  Wassim M. Haddad,et al.  Non-linear impulsive dynamical systems. Part I: Stability and dissipativity , 2001 .

[25]  W. P. M. H. Heemels,et al.  An LMI-based L2 gain performance analysis for reset control systems , 2008, 2008 American Control Conference.

[26]  Rafal Goebel,et al.  Lyapunov characterization of Zeno behavior in hybrid systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[27]  J. C. Clegg A nonlinear integrator for servomechanisms , 1958, Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry.

[28]  Luca Zaccarian,et al.  Stability properties of reset systems , 2008, Autom..

[29]  Wassim M. Haddad,et al.  Energy-based control for hybrid port-controlled Hamiltonian systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[30]  A. Teel,et al.  DIRECT DESIGN OF ROBUSTLY ASYMPTOTICALLY STABILIZING HYBRID FEEDBACK , 2009 .