Disturbance Rejection With Simultaneous Input-Output Linearization and Decoupling Via Restricted State Feedback

The disturbance rejection with simultaneous input-output linearization and decoupling problem of nonsquare nonlinear systems via restricted state feedback is investigated in this paper. The problem is treated on the basis of an algebraic approach whose main feature is that it reduces the determination of the admissible state feedback control laws to the solution of an algebraic and a first order partial differential systems of equations. Verifiable necessary and sufficient conditions of algebraic nature based on these systems of equations are established for the solvability of the aforementioned problem. Moreover, an explicit expression for a special admissible restricted state feedback controller is analytically derived.

[1]  K. Arvanitis.  UNIFORM DECOUPLING BY RESTRICTED STATIC STATE FEEDBACK FOR LINEAR TIME-VARYING ANALYTIC SYSTEMS , 1998 .

[2]  K. Arvanitis.  Simultaneous uniform disturbance rejection and decoupling for nonsquare linear time-dependent analytic systems using restricted state feedback , 1997 .

[3]  K. Arvanitis.  Uniform disturbance localization with simultaneous uniform decoupling for linear time-varying analytic systems , 1994 .

[4]  J. Lafay,et al.  New results about Morgan's problem , 1993, IEEE Trans. Autom. Control..

[5]  X. Xia.  Parameterization of decoupling control laws for affine nonlinear systems , 1993, IEEE Trans. Autom. Control..

[6]  Alain Glumineau,et al.  Nonlinear Morgan's problem: case of (p+1) inputs and p outputs , 1992 .

[7]  Henri Huijberts,et al.  A nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem , 1992 .

[8]  T. Narikiyo,et al.  On Model Feedback Control for Robot Manipulators , 1991 .

[9]  T. Tarn,et al.  INPUT-OUTPUT DECOUPLING AND LINEARIZATION VIA RESTRICTED STATIC-STATE FEEDBACK , 1990 .

[10]  Bong Wie,et al.  New approach to attitude/momentum control for the Space Station , 1989 .

[11]  J. Descusse,et al.  Solution to Morgan's problem , 1988 .

[12]  J. Descusse,et al.  A survey on Morgan's problem , 1986, 1986 25th IEEE Conference on Decision and Control.

[13]  J. Descusse,et al.  New decoupling invariants: the essential orders , 1986 .

[14]  I. Ha,et al.  A complete characterization of decoupling control laws for a general class of nonlinear systems , 1986 .

[15]  Aldo Isidori.  Nonlinear Control Systems: An Introduction , 1986 .

[16]  A. Krener.  $({\text{Ad}}_{f,g} )$, $({\text{ad}}_{f,g} )$ and Locally $({\text{ad}}_{f,g} )$ Invariant and Controllability Distributions , 1985 .

[17]  A. Van,et al.  The disturbance decoupling problem for nonlinear control systems , 1983 .

[18]  A. Isidori,et al.  Nonlinear decoupling via feedback: A differential geometric approach , 1981 .

[19]  K. Furuta,et al.  Decoupling by restricted state feedback , 1976 .

[20]  W. Porter.  Decoupling of and inverses for time-varying linear systems , 1969 .

[21]  P. Falb,et al.  Decoupling in the design and synthesis of multivariable control systems , 1967, IEEE Transactions on Automatic Control.

[22]  Jr. B. Morgan.  The synthesis of linear multivariable systems by state-variable feedback , 1964 .

[23]  J. Descusse,et al.  Decoupling by restricted static-state feedback: The general case , 1984 .

[24]  R. Hirschorn.  $(A,\mathcal{B})$-Invariant Distributions and Disturbance Decoupling of Nonlinear Systems , 1981 .

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