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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 thisExpand
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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, theExpand
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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 fewExpand
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Transcriptional control of human p53-regulated genes
The p53 protein regulates the transcription of many different genes in response to a wide variety of stress signals. Following DNA damage, p53 regulates key processes, including DNA repair,Expand
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Mathematical Control Theory: Deterministic Finite Dimensional Systems
Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. Expand
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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 basicExpand
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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 earlierExpand
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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 ISSExpand
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A Smooth Converse Lyapunov Theorem for Robust Stability
This paper presents a converse Lyapunov function theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems.Expand
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New characterizations of input-to-state stability
We present new characterizations of the input-to-state stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variationsExpand
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