[PDF] Top 20 Robust Stability of Implicit Dynamic Equations on Time Scales

... the robust stability of these ...the robust stability analysis, (see [8, 9]). For the stability theory of time-varying linear DAEs, a few contributions are available (see [10, ... See full document

... Leontiev dynamic model of multisector economy, the Leslie population growth model, and singular discrete optimal control ...differential-algebraic equations, and so forth, which have already attracted much ... See full document

... The concept of time scales analysis is a fairly new idea. In 1988, it was introduced by the German mathematician Stefan Hilger in his Ph.D. thesis [12]. It combines the traditional areas of continuous and ... See full document

... for dynamic equations on time scales, which generalize the corresponding results on differential and difference ...theory, stability, disconjugacy, eigenvalue problems and numerous ... See full document

... is considered by using a type I Lyapunov function. Then, in [5], the authors considered nonnegative definite Lyapunov functions and obtained sufficient conditions for the ex- ponential stability of the zero ... See full document

... the stability characteristics of a nonautonomous linear system of differential or difference equations can be characterized completely by a corresponding autonomous linear system by the Lyapunov ... See full document

... and stability of delay dynamic equations on time ...for dynamic equations can be found in the articles [6–23] and the references cited ... See full document

... In the sequel, we denote by T ⊆ R ≥ for a time scale which is an additive semigroup with the property that a – b ∈ T for any a, b ∈ T such that a > b. In this case, T is called a semigroup time scale. ... See full document

... Remark 2.9. Comparing Lemmas 2.7 and 1.5 we see that nabla exponential functions ap- proach zero in the larger region (see (1.25)) in the complex plane than delta exponential functions (see (2.87)). Thus asymptotic ... See full document

... Note that V = V (x) and even if the vector field associated with the dynamic equation is autonomous, ˙ V still depends on t (and x of course) when the graininess function of T is nonconstant. Several formulas are ... See full document

... The aim of this paper is to present some new Gronwall- Bellman type fractional integral inequalities and Volterra- Fredholm type fractional integral inequalities for the sake of researching qualitative and quantitative ... See full document

... of dynamic equations on time scales, which has recently received a lot of attention, was introduced by Hilger in his ...of time scale, that is, measure chain, by Bohner and Peterson ... See full document

... nonautonomous equations have exponential dichotomy on time scales if and only if its associative operator is ...on time scales by ... See full document

... Existence results for system (1.2) were obtained in [5] with f is a continuous function. In the particular case where n = 1, existence results for first-order ∇-dynamic equation on time scales were ... See full document

... Now a suitable application of Lemma to (4.24) yields (4.22) which shows the dependency of solutions of initial boundary value problem (4.16) − (4.17) and initial boundary value problem (4.17) − (4.18) on parameters. ... See full document

... The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to a nonlinear impulsive dynamic equation with homogeneous Dirichlet ... See full document

... and applied to the solution of ordinary differential equations in the control engineering problems (see also [2]). It appeared like the modification of the Laplace transform. The Sumudu transform rivals the ... See full document

... A time scale is an arbitrary non-empty closed subset of the real numbers ...the time scale under consideration is not bounded above, i.e., it is a time scale interval of the form ...any time ... See full document

... differential equations, difference equations, dynamic equations on time scales, p-Laplacian, fractional order differential equations and boundary value ... See full document

... compact. In view of Lebesgue’s dominated convergence theorem on time scales [7], it is easy to prove that T is continuous. Hence, T is completely continuous. Theorem 2.1. [Krasnosel’skii] [13, 20] Let B be ... See full document