On the stabilization of nonlinear systems

We extend the applicability of the global Q-parametrization method of controller design to a large class of unstable nonlinear plants. The main result is a two-step compensation theorem analogous to that of Zames for unstable linear plants - if P:Le2 ¿ Le1 is a nonlinear (possibly unstable) plant and Fo is any incrementally stable controller such that P1:= P(I-Fo(-P))-1 is incrementally stable, then the class of controllers F which yield a f.g. stable closed-loop system in the unity feedback configuration for P, is globally parametrized by finite gain stable maps Q: Li1 ¿ Le2 with F = Fo + Q(I-P1Q)-1.

[1]  D. Youla,et al.  Single-loop feedback-stabilization of linear multivariable dynamical plants , 1974, Autom..

[2]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[3]  C. Desoer,et al.  The feedback interconnection of multivariable systems: Simplifying theorems for stability , 1976, Proceedings of the IEEE.

[4]  C. Desoer,et al.  Feedback system design: The fractional representation approach to analysis and synthesis , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[5]  V. Cheng,et al.  Limitations on the closed-loop transfer function due to right-half plane transmission zeros of the plant , 1980 .

[6]  L. Pernebo.  An algebraic theory for design of controllers for linear multivariable systems--Part II: Feedback realizations and feedback design , 1981 .

[7]  C. Desoer,et al.  Global parametrization of feedback systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[8]  C. Desoer,et al.  Design of multivariable feedback systems with stable plant , 1981 .

[9]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[10]  C. Desoer,et al.  Global parametrization of feedback systems with nonlinear plants , 1982 .

[11]  C. Gustafson,et al.  A CAD methodology for linear multivariable feedback systems based on algebraic theory , 1983, The 22nd IEEE Conference on Decision and Control.

[12]  Charles A. Desoer,et al.  Controller Design for Linear Multivariable Feedback Systems with Stable Plants, Using Optimization with Inequality Constraints , 1983 .