A canonical dynamic extension for noninteraction with stability for nonlinear systems

The problem of noninteracting control with stability via dynamic feedback is considered for nonlinear systems with two inputs and two outputs. Given a system which may not be capable of decoupling via static state feedback but is capable of decoupling via dynamic feedback, a canonical dynamic extension is constructed. It is shown that every dynamic extension contains this canonical one. Hence, the Delta /sub mix/ dynamics as defined by K. Wagner (1989) of the canonical extension is contained in every other dynamic extension. Following Wagner's result, the stability of this Delta /sub mix/ dynamics is necessary for noninteraction with internal stability. The results obtained show that in the investigation of noninteraction with stability one can assume without loss of generality that the system is capable of decoupling via static state feedback.<<ETX>>

[1]  Alberto Isidori,et al.  Block noninteracting control with stability via static state feedback , 1989, Math. Control. Signals Syst..

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

[3]  J. Descusse,et al.  Dynamic decoupling for right-invertible nonlinear systems , 1987 .

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

[5]  A. Isidori.  Nonlinear Control Systems , 1985 .

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

[7]  A. Morse,et al.  Decoupling and pole assignment by dynamic compensation , 1970 .

[8]  J. Descusse,et al.  Decoupling with Dynamic Compensation for Strong Invertible Affine Non Linear Systems , 1985 .

[9]  Elmer G. Gilbert,et al.  The Decoupling of Multivariable Systems by State Feedback , 1969 .

[10]  H. Nijmeijer,et al.  Dynamic input-output decoupling of nonlinear control systems , 1988 .

[11]  K. Wagner,et al.  On nonlinear noninteraction with stability , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

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

[13]  A. Morse,et al.  Status of noninteracting control , 1971 .

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

[15]  Stefano Battilotti,et al.  A sufficient condition for nonlinear noninteracting control with stability via dynamic state feedback , 1991 .

[16]  H. Sussmann,et al.  Controllability of nonlinear systems , 1972 .

[17]  A. Isidori,et al.  Fixed modes and nonlinear noninteracting control with stability , 1988 .