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… (More)

We show that the well-known Lyapunov sufficient condition for “input-to-state stability” is also necessary, settling positively an open question raised by several authors during the past few years.… (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… (More)

so that inf (LrV(x) + UlLgV(x) tier m 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… (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… (More)

This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L∞… (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… (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… (More)

with states z ( t ) evolving in Euclidean space EL” and controls U ( . ) taking values u(t) E W & Et” for some positive integers w and m (in all the main results, W = R”). The questions to be… (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… (More)