Stabilization of Nonlinear Systems and Coprime Factorization

Verma, M.S.; Pham, Tho D.

doi:10.1007/978-1-4612-4484-4_46

Cited by 5 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(4.20) It is now possible to construct a stable right factorization for (2 (zO) as is explored in the following lemma. This lemma is equivalent to T leorem 3 of [22], and parallels the discrete time results found in [8].…”

Section: Assumptionsupporting

confidence: 73%

See 2 more Smart Citations

Nonlinear Feedback System Stability via Coprime Factorization Analysis

Paice

Moore

Horowitz

1992

1992 American Control Conference

View full text Add to dashboard Cite

In this paper right coprime factorization results are derived for i. general class of nonlinear plants and stabilizing feedback controllers Both input-output descriptions and state space realizations of th(plant and controller are used. It is first shown that if there exist stable right coprime factorizt ions for the plant and controller, and if a certain matrix of nonlinear operators has a stable inverse then the feedback system is well-posed and internally stable. The links between the right and left coprime factorization for a stable plant controller pair will be explored for this purpose. A generalization of the notion of linear fractional maps is explored as a means of characterizing the class of plants stabilized by this controller, and dually classes of controllers which stabilize the plant. It is then shown how to apply this theory to nonlinear plants which have a state space realization of a given form. It is also shown that if there exists a stabilizing state feedback for a plant in the class of int crest, then there exists a right cop rime factorization for the plant. Additionidly if there exists a stabilizing output injection, then there will exist a stabilizing controller with a right coprime factorization. An important sasumption in this work is to assume that the plant and controller have the same initial conditions, an approach is developed to allow for the stabfization of the plant by a controller with a different initial condition. A similar approach may also be used to stabilize a plant which has unmodeled dynamics. These results, of course, specialize to familiar linear system ones, and just as such linear systems results have had a wide application in robust and adaptive control system design, it is believed that the results developed here will facilitate the development of corresponding nonlinear robust and adaptive control system design.

show abstract

Section: Assumptionsupporting

confidence: 73%

“…In [22] Verma presented a construction of the right coprime factorization of a ger eral continuous time nonlinear plant, while in [8] Hammer gives a construe tion for discrete time systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Feedback System Stability via Coprime Factorization Analysis

Paice

Moore

Horowitz

1992

1992 American Control Conference

View full text Add to dashboard Cite

show abstract

“…A number of authors have tried to extend these results to nonlinear systems, for example Hammer [3, 4, 51, Chen [l, 21, Moore and co-workers [7, 61 and Verma [16,17,181. None of these works proved a fully satisfactory nonlinear version of the linear results, in that either state space expressions were not available, or the Youla parameterization could not be fully derived.…”

Section: Introductionmentioning

confidence: 99%