# Smooth stabilization implies coprime factorization

@article{Sontag1989SmoothSI, title={Smooth stabilization implies coprime factorization}, author={Eduardo Sontag}, journal={IEEE Transactions on Automatic Control}, year={1989}, volume={34}, pages={435-443} }

It is shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. It follows that feedback linearizable systems admit such fabrications. In order to establish the result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stability studied in the state-space nonlinear control literature is related to a…

## 2,341 Citations

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A technique is developed that allows state and input constraints for a feedback linearizable system to be mapped to the equivalent linear system.

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New definitions for the right, left and doubly-coprime factorizations for nonlinear, input-affine systems based on the notion of the state-to-output stability are introduced. Sufficient conditions…

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- 1992

In this paper we describe a family of operators for constructing nontrivial left and right coprime factorizations under rather weak conditions for a large class of nonlinear feedback control systems…

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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…

Nonlinear Feedback System Stability via Coprime Factorization Analysis

- Mathematics1992 American Control Conference
- 1992

In this paper right coprime factorization results are derived for a general class of nonlinear plants and stabilizing feedback controllers. Both input-output descriptions and state space realizations…

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The problem of constructing right coprime factorizations of a nonlinear system is considered. It is assumed that the nonlinear system is specified in terms of a state-space realization, which is I/O…

On the Construction of Coprime Factorization of Nonlinear Feedback Control Systems

- Mathematics1990 American Control Conference
- 1990

In this paper, we present a new approach for constructing left and right coprime factorizations for a large class of (stable and unstable) nonlinear feedback control systems developed recently by the…

Output-input stability implies feedback stabilization

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Coprime Factorization over a Class of Nonlinear Systems

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- 1992

In this paper, we consider the problem of generalizing elements of linear coprime factorization theory to nonlinear systems characterized in terms of (possibly time varying) state dependent matrices…

INPUT TO STATE STABILIZABILITY FOR PARAMETRIZED FAMILIES OF SYSTEMS

- Mathematics
- 1995

SUMMARY This paper studies various stability issues for parametrized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust…

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