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Smooth stabilization implies coprime factorization
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
A universal construction of Artstein's theorem on nonlinear stabilization
Abstract This note presents an explicit proof of the theorem - due to Artstein - which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. Moreover, the
Mathematical Control Theory: Deterministic Finite Dimensional Systems
TLDR
This book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects, covering a wide range of topics written in a standard theorem/proof style and develops the necessary techniques from scratch.
On characterizations of the input-to-state stability property
We show that the well-known Lyapunov sufficient condition for "input-to-state stability" (ISS) is also necessary, settling positively an open question raised by several authors during the past few
Transcriptional control of human p53-regulated genes
TLDR
The most comprehensive list so far of human p53-regulated genes and their experimentally validated, functional binding sites that confer p53 regulation is presented.
Input to State Stability: Basic Concepts and Results
The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic
Input-to-state stability for discrete-time nonlinear systems
Abstract In this paper the input-to-state stability (ISS) property is studied for discrete-time nonlinear systems. We show that many ISS results for continuons-time nonlinear systems in earlier
Comments on integral variants of ISS
Abstract This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L 2 stability, in much the same way that ISS
New characterizations of input-to-state stability
TLDR
New characterizations of the input-to-state stability property are presented and the equivalence between the ISS property and several (apparent) variations proposed in the literature are shown.
A characterization of integral input-to-state stability
TLDR
The notion of iISS generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear "H/sup 2/" theory.
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