On functional observers for linear systems with unknown inputs and HOSM differentiators

Abstract The problem of constructing functional observers for linear systems with unknown inputs is considered. Necessary and sufficient conditions for the existence of a proper observer (without differentiations) are revisited. A simple and explicit form of a functional observer is presented. It is shown that when such observer is not proper, it is still possible to use the High-Order Sliding Mode differentiator to implement it. Nevertheless, in such case, additional conditions on the system and the unknown input are required.

[1]  Barbara Zitov a.  Journal of the Franklin Institute , 1942, Nature.

[2]  T. Boukhobza,et al.  High order sliding modes , 1998 .

[3]  Sarah K. Spurgeon,et al.  Sliding mode observers: a survey , 2008, Int. J. Syst. Sci..

[4]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[5]  P. Sannuti,et al.  A special coordinate basis of multivariable linear systems- Finite and infinite zero structure , 1986, 1986 25th IEEE Conference on Decision and Control.

[6]  Jie Chen,et al.  Observer-based fault detection and isolation: robustness and applications , 1997 .

[7]  Arie Levant,et al.  Exact Differentiation of Signals with Unbounded Higher Derivatives , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[8]  J. Moreno,et al.  Quasi-unknown input observers for linear systems , 2001, Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204).

[9]  Tyrone Fernando,et al.  Design of reduced-order state/unknown input observers based on a descriptor system approach , 2010 .

[10]  S. Żak,et al.  State observation of nonlinear uncertain dynamical systems , 1987 .

[11]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[12]  B. Molinari.  A strong controllability and observability in linear multivariable control , 1976 .

[13]  Ali Saberi,et al.  Special coordinate basis for multivariable linear systems—finite and infinite zero structure, squaring down and decoupling , 1987 .

[14]  Christopher Edwards,et al.  Circumventing the Relative Degree Condition in Sliding Mode Design , 2008 .

[15]  Alexander S. Poznyak,et al.  Observation of linear systems with unknown inputs via high-order sliding-modes , 2007, Int. J. Syst. Sci..

[16]  Robert Engel,et al.  A continuous-time observer which converges in finite time , 2002, IEEE Trans. Autom. Control..

[17]  Yuri B. Shtessel,et al.  Editorial 2: Sliding mode observation and identification , 2007, Int. J. Syst. Sci..

[18]  Harry L. Trentelman,et al.  Control theory for linear systems , 2002 .

[19]  Vadim I. Utkin,et al.  Sliding mode control , 2004 .

[20]  Tyrone Fernando,et al.  Design of Reduced-Order Functional Observers for Linear Systems with Unknown Inputs , 2008 .

[21]  Andrzej Bartoszewicz,et al.  Sliding Mode Control , 2007 .

[22]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[23]  M. Hautus.  Strong detectability and observers , 1983 .

[24]  Leonid M. Fridman,et al.  High order sliding mode observer for linear systems with unbounded unknown inputs , 2010, Int. J. Control.

[25]  T. Floquet,et al.  On Sliding Mode Observers for Systems with Unknown Inputs , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..