[show abstract][hide abstract] ABSTRACT: The input-to-state stability of time invariant systems described by coupled delay differential and difference equations is here investigated. A new Liapunov-Krasovskii theorem to check such type of stability is proved. An example taken from the literature, concerning an electrical circuit, is reported, showing the effectiveness of the methodology.
Decision and Control, 2007 46th IEEE Conference on; 01/2008
[show abstract][hide abstract] ABSTRACT: The input-to-state stability of time-invariant systems described by coupled differential and difference equations with multiple noncommensurate and distributed time delays is investigated in this paper. Such equations include neutral functional differential equations in Hale’s form (which model, for instance, partial element equivalent circuits) and describe lossless propagation phenomena occurring in thermal, hydraulic and electrical engineering. A general methodology for systematically studying the input-to-state stability, by means of Liapunov–Krasovskii functionals, with respect to measurable and locally essentially bounded inputs, is provided. The technical problem concerning the absolute continuity of the functional evaluated at the solution has been studied and solved by introducing the hypothesis that the functional is locally Lipschitz. Computationally checkable LMI conditions are provided for the linear case. It is proved that a linear neutral system in Hale’s form with stable difference operator is input-to-state stable if and only if the trivial solution in the unforced case is asymptotically stable. A nonlinear example taken from the literature, concerning an electrical device, is reported, showing the effectiveness of the proposed methodology.
[show abstract][hide abstract] ABSTRACT: In this paper a new Lyapunov-Krasovskii methodology for nonlinear coupled delay dif-ferential di®erence equations is proposed. This method-ology is based on the concept of input-to-state stability applied to the di®erence equation, for which a su±cient Lyapunov criterion is given, and on previous method-ologies developed in the literature for linear delay de-scriptor systems.
International Journal of Control - INT J CONTR. 01/2008; 81(1).
[show abstract][hide abstract] ABSTRACT: This paper presents a Lyapunov-Krasovskii methodology for studying the input-to-state stability of nonlinear time-delay systems. The methodology is feasible by the use, for instance, of the M 2 norm (that is the norm induced by the inner product in the Hilbert space known in literature as M 2 , or Z) in the space of continuous functions, and by the use of functionals which have a suitable (simple) integral term with strictly increasing kernel. The proposed results can be seen as a preliminary step towards extending some existing stability criteria to nonlinear time-delay systems with disturbance inputs.
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on; 01/2006
[show abstract][hide abstract] ABSTRACT: This paper presents a Lyapunov–Krasovskii methodology for studying the input-to-state stability and the integral input-to-state stability of nonlinear time-delay systems. An integral input-state estimate which takes into account non-zero initial conditions is also proposed.