The class of stabilizing nonlinear plant controller pairs

In this paper a general approach is taken to yield a characterization of the class of stable plant controller pairs which is a generalization of the Youla parameterization for linear systems. This is based on the idea of representing the input-output pairs of the plant and controller as elements of the kernel of some related operator which is denoted the kernel representation of the system. It is demonstrated that in some sense the kernel representation is a generalization of the left coprime factorization of a general nonlinear system. Results giving one method of deriving a kernel representation for a nonlinear plant with a general state-space description are presented.

[1]  C. Jacobson,et al.  A connection between state-space and doubly coprime fractional representations , 1984 .

[2]  Eduardo D. Sontag.  Some connections between stabilization and factorization , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[3]  Rui J. P. de Figueiredo,et al.  On construction of coprime factorizations for nonlinear feedback control systems , 1992 .

[4]  Mathukumalli Vidyasagar.  Normalised coprime factorizations for nonstrictly proper systems , 1988 .

[5]  John B. Moore,et al.  Robust stabilisation of nonlinear plants via left coprime factorizations , 1990 .

[6]  Jan C. Willems,et al.  Feedback in a Behavioral Setting , 1992 .

[7]  A. Paice.  Stabilization and identification of nonlinear systems , 1992 .

[8]  Jan C. Willems,et al.  Models for Dynamics , 1989 .

[9]  Madanpal S. Verma,et al.  Coprime fractional representations and stability of non-linear feedback systems , 1988 .

[10]  O. V. Anashkin,et al.  On Stabilization of Nonlinear Systems , 1996 .

[11]  D. Meyer,et al.  A connection between normalized coprime factorizations and linear quadratic regulator theory , 1987 .

[12]  J. Willems.  Paradigms and puzzles in the theory of dynamical systems , 1991 .

[13]  Louis R. Hunt,et al.  Right coprime factorizations and stabilization for nonlinear systems , 1993, IEEE Trans. Autom. Control..

[14]  Guanrong Chen,et al.  A necessary and sufficient condition for right coprime factorization of nonlinear feedback systems , 1993 .

[15]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[16]  John B. Moore,et al.  On the Youla-Kucera parametrization for nonlinear systems , 1990 .

[17]  B. Francis,et al.  A Course in H Control Theory , 1987 .

[18]  J. Hammer.  Internally stable nonlinear systems with disturbances: a parameterization , 1994, IEEE Trans. Autom. Control..

[19]  John B. Moore,et al.  Robust stabilization of nonlinear plants via left coprime factorizations , 1990, 29th IEEE Conference on Decision and Control.

[20]  John B. Moore,et al.  Indirect adaptive techniques for fixed controller performance enhancement , 1989 .

[21]  Stabilization of Nonlinear Systems and Coprime Factorization , 1990 .

[22]  A theory of stabilization for nonlinear systems , 1986, 1986 25th IEEE Conference on Decision and Control.

[23]  John B. Moore,et al.  Left coprime factorizations and a class of stabilizing controllers for nonlinear systems , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[24]  John B. Moore,et al.  Left coprime factorizations and a class of stabilizing controllers for non-linear systems , 1989 .

[25]  Jacob Hammeri,et al.  Non-linear systems, stabilization, and coprimeness† , 1985 .

[26]  Jacob Hammer,et al.  Non-linear systems: stability and rationality , 1984 .

[27]  J. B. Moore,et al.  Coprime Factorization over a Class of Nonlinear Systems , 1992, 1992 American Control Conference.

[28]  van der Arjan Schaft,et al.  Normalized coprime factorizations and balancing for unstable nonlinear systems , 1994 .