On estimating regions of stability of the estimation error of sliding mode observers for uncertain systems

Two classes of full-order sliding mode observers for uncertain dynamical systems are analyzed. The first class has its roots in the sliding mode equivalent-control method, while the second class is based on the second method of Lyapunov. The observers are analyzed using differential inequalities that appear in the analysis of a class of sliding mode controllers. Using the differential inequalities, regions of stability of the estimation error are determined. In addition, uniform ultimate boundedness of the estimation error is proven for the equivalent-control based class of sliding mode observers for uncertain dynamical systems

[1]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[2]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[3]  Stefen Hui,et al.  Control and Observation of Uncertain Systems: A Variable Structure Systems Approach , 1990 .

[4]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[5]  Jie Chen,et al.  Design of unknown input observers and robust fault detection filters , 1996 .

[6]  Stefen Hui,et al.  Robust control synthesis for uncertain/nonlinear dynamical systems , 1992, Autom..

[7]  M. Chung,et al.  Estimation of the asymptotic stability region of uncertain systems with bounded sliding mode controllers , 1994, IEEE Trans. Autom. Control..

[8]  M. Hou,et al.  Design of observers for linear systems with unknown inputs , 1992 .

[9]  S. Żak,et al.  Observer design for systems with unknown inputs , 2005 .

[10]  Martin J. Corless,et al.  State and Input Estimation for a Class of Uncertain Systems , 1998, Autom..

[11]  Mehrdad Saif,et al.  Sliding Mode Observers and Their Application in Fault Diagnosis , 2003 .

[12]  F. Fairman.  Introduction to dynamic systems: Theory, models and applications , 1979, Proceedings of the IEEE.

[13]  Stefen Hui,et al.  On the estimation of sliding domains and stability regions of variable structure control systems with bounded controllers , 1993 .

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

[15]  Stanislaw H. Żak,et al.  Practical stabilization of nonlinear/uncertain dynamic systems with bounded controllers , 1995 .

[16]  M. Corless,et al.  Stabilizing uncertain systems with bounded control , 1991 .

[17]  Stefen Hui,et al.  Robust Output Feedback Stabilization of Uncertain Dynamic Systems with Bounded Controllers , 1992, 1992 American Control Conference.

[18]  Mehrez Hached,et al.  Estimation of sliding mode domains of uncertain variable structure systems with bounded controllers , 1990 .