1,721,130 research outputs found
On Sontag's formula for the input-to-state practical stabilization of retarded control-affine systems
No full text
The Problem of the Absolute Continuity for Lyapunov-Krasovskii Functionals
No full textThe condition of nonpositivity, almost everywhere, of the
upper right-hand Dini derivative of a (simply) continuous function is not a
sufficient condition for such function to be nonincreasing. That condition is
sufficient for the nonincreasing property if the function is locally absolutely
continuous. Therefore, if the time function obtained by the evaluation of
a Lyapunov–Krasovskii functional at the solution of a time-delay system
is not locally absolutely continuous, but simply continuous, and its upper
right-hand Dini derivative is almost everywhere nonpositive, then the
conclusion that such function is nonincreasing cannot be drawn. As a
consequence, related stability conclusions cannot be drawn. In this note,
such problem is investigated for input-to-state stability concerns of time
invariant time-delay systems forced by measurable locally essentially
bounded inputs. It is shown that, if the Lyapunov–Krasovskii functional
is locally Lipschitz with respect to the norm of the uniform topology, then
the problem of the absolute continuity is overcome
On Liapunov-Krasovskii Functionals under Carathéodory Conditions
No full textIn [Driver, R. D. (1962). Existence and stability of solutions of a delay-differential system. Archive for Rational Mechanics and Analysis
10, 401–426] a proper definition, not involving the solution, of the derivative of the Liapunov–Krasovskii functional for retarded functional
differential equations with continuous right side is given and it is showed that this definition coincides with the non-constructive one given
in Krasovskii [1956. On the application of the second method of A. M. Lyapunov to equations with time delays (in Russian). Prikladnaya
Matematika i Mekhanika 20, 315–327] involving the solution, for functionals V which are locally Lipschitz (and not only continuous, as it is
considered in most literature). In this paper, the result by Driver is extended to a general class of retarded functional differential equations
coupled with continuous time difference equations with more general right sides, verifying the Carathéodory conditions. Such result is applied
to build a new Liapunov–Krasovskii theorem for studying the input-to-state stability of time-invariant neutral functional differential equations
with linear difference operator. An example taken from the literature, concerning transmission lines, is reported, showing the effectiveness of
the methodology
On the Asymptotic Stability of Coupled Delay Differential and Continuous Time Difference Equations
No full text
Stabilization of retarded systems of neutral type by control Lyapunov–Krasovskii functionals
No full textThis paper deals with the stabilization and the practical stabilization of nonlinear systems described by neutral functional differential equations in Hale's form, affine in the control input. Artstein's methodology and Sontag's universal formula are investigated for this class of systems, by means of invariantly differentiable control Lyapunov–Krasovskii functionals
- …
