Hybrid‐type observer design based on a sufficient condition for observability in switched nonlinear systems

This paper presents a sufficient condition for observability of continuous‐time switched nonlinear systems that also involve state jumps. Without the assumption of observability of individual modes, the sufficient condition is based on gathering partial information from each mode so that the state is completely recovered after several switchings. Based on the sufficient condition, a hybrid‐type observer is designed, which comprises a copy of the actual plant and an error correction scheme at discrete time instants. In order to execute the proposed design, the observable component of the state at each mode needs to be estimated without transients or ‘peaking’ (caused by high‐gain observers), and this motivates us to introduce a back‐and‐forth estimation technique. Under the assumption of persistent switching, analysis shows that the estimate thus generated converges asymptotically to the actual state of the system. Simulation results validate the utility of the proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  G. Basile,et al.  Controlled and conditioned invariant subspaces in linear system theory , 1969 .

[2]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[3]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[4]  J. Gauthier,et al.  Observability and observers for non-linear systems , 1986, 1986 25th IEEE Conference on Decision and Control.

[5]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[6]  P. Kokotovic,et al.  The peaking phenomenon and the global stabilization of nonlinear systems , 1991 .

[7]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[8]  H. Khalil,et al.  Output feedback stabilization of fully linearizable systems , 1992 .

[9]  A. Teel,et al.  Global stabilizability and observability imply semi-global stabilizability by output feedback , 1994 .

[10]  Hyungbo Shim,et al.  Non-linear output feedback stabilization on a bounded region of attraction , 2000 .

[11]  심형보.  A passivity-based nonlinear observer and a semi-global separation principle , 2000 .

[12]  H. Shim,et al.  Semi-global observer for multi-output nonlinear systems , 2001 .

[13]  A. Alessandri,et al.  Switching observers for continuous-time and discrete-time linear systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[14]  J. Gauthier,et al.  Deterministic Observation Theory and Applications , 2001 .

[15]  Observability for hybrid systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[17]  Jan H. van Schuppen,et al.  Observability of Piecewise-Affine Hybrid Systems , 2004, HSCC.

[18]  Guangming Xie,et al.  Necessary and sufficient conditions for controllability and observability of switched impulsive control systems , 2004, IEEE Transactions on Automatic Control.

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

[20]  Shuzhi Sam Ge,et al.  Switched Linear Systems , 2005 .

[21]  Stefan Pettersson.  Designing switched observers for switched Systems using Multiple Lyapunov Functions and dwell-Time switching , 2006, ADHS.

[22]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[23]  J. Barbot,et al.  Nonlinear Observer for Autonomous Switching Systems with Jumps , 2007 .

[24]  Wei Kang,et al.  On the Observability of Nonlinear and Switched Systems , 2009 .

[25]  Hyungbo Shim,et al.  On a sufficient condition for observability of nonlinear switched systems and observer design strategy , 2011, Proceedings of the 2011 American Control Conference.

[26]  Michael Defoort,et al.  Robust finite time observer design for multicellular converters , 2011, Int. J. Syst. Sci..

[27]  Hyungbo Shim,et al.  Observability implies observer design for switched linear systems , 2011, HSCC '11.

[28]  Hyungbo Shim,et al.  Observability for Switched Linear Systems: Characterization and Observer Design , 2013, IEEE Transactions on Automatic Control.

[29]  A. D. Mahindrakar,et al.  Nonlinear Control System , 2014 .