At the occasion of Eduardo D. Sontag’s 70th birthday, we provide here an overview tools available to study input-to-state stability (ISS) and related notions for time-delay systems. After a hopefully pedagogical presentation main differences with respect finite-dimensional theory, review basic concepts input-free systems, as well instruments guarantee them in practice, including Lyapunov–Krasov...

In April 2010 the International Finance Corporation announced the creation of the African, Latin American, and Caribbean fund, a new co-investment vehicle funded largely with commitments from sovereign wealth and pension funds. The fund’s objective was to draw on the IFC and the World Bank’s strengths in emerging markets to identify and support enterprises that might not otherwise have come to ...

For a bar and joint framework (G, p) with point group C3 which describes 3-fold rotational symmetry in the plane, it was recently shown in (Schulze, Discret. Comp. Geom. 44:946-972) that the standard Laman conditions, together with the condition derived in (Connelly et al., Int. J. Solids Struct. 46:762-773) that no vertices are fixed by the automorphism corresponding to the 3-fold rotation (ge...

Observation of writers producingg non-trivial texts suggests t hat most spendd time generating andd organisingg content prior to draftingg full text. Resear chsuggests a linkk between time spent inn these activities andd the quality of the resulting docume nt. Very little is known, however, about either the nature of the representation that is c reatedd during this planningg phase (the writer's...

It is well known that stability of Hopfield type neural networks plays a very important role in both theoretical research and applications. So, it has been kept on studying in two decades. Stochastic effectiveness to this kind of neural networks has also received a lot of attention (ref. [Liao et al, 1996 A], [Liao et al, 1996 B], [Blythe,S. et al, 2001A] and [Blythe,S. et al, 2001B]). In this ...

We propose a mathematical model describing the dynamics of a hematopoietic stem cell population. The method of characteristics reduces the age-structured model to a system of differential equations with a state-dependent delay. A detailed stability analysis is performed. A sufficient condition for the global asymptotic stability of the trivial steady state is obtained using a Lyapunov–Razumikhi...

This paper considers a sliding mode control of multivariable nonlinear systems with time-varying delay. In our previous work, a sliding mode control design method combining with the finite spectrum assignment has been developed. In the design method, the sliding surface is constructed by using a coordinates transformation containing past values of the state variables. In most practical systems,...

In this paper, upper bounds for time-varying delays in the real-time control of a lab helicopter in the sense of practical stability analysis are derived. Sub-optimal controller parameters for this non-linear plant with a given maximum time-delay are calculated with the help of Lyapunov-Razumikhin method using LMIs (Linear Matrix Inequalities). These parameters are then optimized for extended t...

This paper is concerned with the problem of exponential stability for a class of impulsive nonlinear stochastic differential equations with mixed time delays. By applying the Lyapunov–Krasovskii functional, Dynkin formula and Razumikhin technique with a stochastic version as well as the linear matrix inequalities (LMIs) technique, some novel sufficient conditions are derived to ensure the expon...