Output feedback variable structure controllers and state estimators for uncertain/nonlinear dynamic systems

In the paper a new class of output feedback variable structure controllers and state estimators (observers) for uncertain/nonlinear dynamic systems with bounded uncertainties and/or nonlinearities are proposed. No statistical information about the uncertain elements is assumed. A variable structure systems (VSS) approach together with the geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed output feedback controllers and state estimators. The role of system zeros in the output feedback stabilisation and state estimation, using the VSS approach, is discussed. Numerical examples included illustrate the feasibility of the proposed stabilisation and state estimation schemes.

[1]  J. Hedrick,et al.  Stable, robust tracking by sliding mode control , 1988 .

[2]  Aldo A. Ferri,et al.  Application of output feedback to variable structure systems , 1989 .

[3]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

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

[5]  D. Luenberger.  Observers for multivariable systems , 1966 .

[6]  H. Kimura.  Pole assignment by gain output feedback , 1975 .

[7]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[8]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[9]  Vadim I. Utkin,et al.  A singular perturbation analysis of high-gain feedback systems , 1977 .

[10]  N. Karcanias,et al.  Poles and zeros of linear multivariable systems : a survey of the algebraic, geometric and complex-variable theory , 1976 .

[11]  R. Marino.  High-gain feedback in non-linear control systems† , 1985 .

[12]  B. A. White,et al.  Applications of output feedback in variable structure control , 1990 .

[13]  Stanislaw H. Zak,et al.  Combined observer-controller synthesis for uncertain dynamical systems with applications , 1988, IEEE Trans. Syst. Man Cybern..

[14]  S. Billings,et al.  Analysis and design of variable structure systems using a geometric approach , 1983 .

[15]  Janisław M. Skowroński,et al.  Control of Nonlinear Mechanical Systems , 1991 .

[16]  B. White.  Some Problems in Output Feedback in Variable Structure Control Systems , 1985 .

[17]  R. Hirschorn.  Invertibility of multivariable nonlinear control systems , 1979 .

[18]  Stanislaw H. Żak,et al.  Output feedback control of uncertain systems in the presence of unmodeled actuator and sensor dynamics , 1989 .

[19]  A. Zinober.  Deterministic control of uncertain systems , 1989, Proceedings. ICCON IEEE International Conference on Control and Applications.

[20]  Edward J. Davison,et al.  A generalization of the output control of linear multivariable systems with unmeasurable arbitrary disturbances , 1975 .

[21]  B. Kouvaritakis,et al.  Geometric approach to analysis and synthesis of system zeros Part 1. Square systems , 1976 .

[22]  D. Luenberger.  An introduction to observers , 1971 .

[23]  Andrzej Ehrenfeucht,et al.  Square Systems , 1994, Fundam. Informaticae.

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

[25]  L. Silverman.  Inversion of multivariable linear systems , 1969 .

[26]  S. Żak,et al.  Robust output feedback stabilization of uncertain dynamic systems with bounded controllers , 1993 .

[27]  J. Hedrick,et al.  Nonlinear Observers—A State-of-the-Art Survey , 1989 .

[28]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.