Eduardo D. Sontag

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This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. In order to establish the result a Lyapunov-theoretic(More)
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 result is extended to the real-analytic and rational cases as well. The proof uses a “universal” formula given by an algebraic function of Lie derivatives; this formula(More)
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone(More)
This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L stability, in much the same way that ISS generalizes L∞ stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than(More)
The notion of input-to-state stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite 2 gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other(More)
The title of this book gives a very good description of its contents and style, although I might have added “Introduction to” at the beginning. The style is mathematical: precise, clear statements (i.e., theorems) are asserted, then carefully proved. The book covers many of the key topics in control theory, except — as the subtitle has warned us — those(More)
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, cell-cycle arrest, senescence and apoptosis, in order to suppress cancer. This Analysis article provides an overview of the current knowledge of p53-regulated genes in(More)
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 conceptual notions, and (2) the identification of classes of systems for which systematic decomposition approaches can result in effective and easily computable(More)
It is becoming increasingly clear that bistability (or, more generally, multistability) is an important recurring theme in cell signaling. Bistability may be of particular relevance to biological systems that switch between discrete states, generate oscillatory responses, or "remember" transitory stimuli. Standard mathematical methods allow the detection of(More)