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}
}
  • Eduardo Sontag
  • Published 1 April 1989
  • Mathematics
  • IEEE Transactions on Automatic Control
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… 
Right coprime factorizations and stabilization for nonlinear systems
TLDR
A technique is developed that allows state and input constraints for a feedback linearizable system to be mapped to the equivalent linear system.
Nonlinear coprime factorizations and parameterization of a class of stabilizing controllers
  • L. Baramov, H. Kimura
  • Mathematics
    Proceedings of 1995 34th IEEE Conference on Decision and Control
  • 1995
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
On construction of coprime factorizations for nonlinear feedback control systems
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
Nonlinear Feedback System Stability via Coprime Factorization Analysis *
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
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
Right coprime factorizations of nonlinear systems
  • M. Verma, L. Hunt
  • Mathematics
    Proceedings of the 28th IEEE Conference on Decision and Control,
  • 1989
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
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
  • D. Liberzon
  • Mathematics, Computer Science
    Syst. Control. Lett.
  • 2004
Coprime Factorization over a Class of Nonlinear Systems
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
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
...
...

References

SHOWING 1-10 OF 56 REFERENCES
Stabilization of a class of nonlinear systems by a smooth feedback control
Stabilization with relaxed controls
Stabilization of non-linear control systems: the role of Newton diagrams
Abstract The stabilization of two-dimensional non-linear control systems is treated, although the main technique is applicable to more general systems. It combines the theory of centre manifolds and
Right factorization of a class of time-varying nonlinear systems
A class of nonlinear continuous-time time-varying plants with a state-space description which has a uniformly completely controllable linear part is considered. For this class, a right factorization
Further facts about input to state stabilization
Previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback is allowed.
Non-linear systems: stability and rationality
The problem of when a non-linear system can be represented as a quotient of two stable non-linear systems is considered. Attention is mainly directed toward nonlinear discrete-time recursive systems,
Fraction representations of non-linear systems: a simplified approach
Abstract A non-linear system Σ has a right fraction representation if it can be represented as Σ = PQ−1, where P and Q are stable systems, and it has a left fraction representation if it can be
Remarks on continuous feedback
  • Eduardo Sontag, H. Sussmann
  • Mathematics
    1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes
  • 1980
We show that, in general, it is impossible to stabilize a controllable system by means of a continuous feedback, even if memory is allowed. No optimality considerations are involved. All state spaces
...
...