In this paper we will establish two different classes of ellipticity criteria, called the L criteria and the L-L criteria respectively, for planar linear Hamiltonian systems with periodic coefficients. The criteria are explicitly expressed using the L and L norms of coefficients and some known Sobolev constants. These results can be considered as the extensions of the famous Lyapunov stability ...

We provide necessary and sucient conditions for psi-conditional as-ymptotic stability of the solution of a linear matrix Lyapunov system and sucientconditions for psi -conditional asymptotic stability of the solution of a rst ordernon-linear matrix Lyapunov system X0 = A(t)X + XB(t) + F(t;X).

This paper considers several explicit formulas for the construction of copositive Lyapunov functions for global asymptotic stability with respect to monotone systems evolving in either discrete or continuous time. Such monotone systems arise as comparison systems in the study of interconnected large-scale nominal systems. A copositive Lyapunov function for such a comparison system can then serv...

This paper presents the robust stability criteria for uncertain genetic regulatory networks with time-varying delays. One key point of the criterion is that the decomposition of the matrix D̃ into D̃ = D̃1 + D̃2. This decomposition corresponds to a decomposition of the delayed terms into two groups: the stabilizing ones and the destabilizing ones. This technique enables one to take the stabilizing ...

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, P.R. China Abstract In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guaran...

We present several equivalent characterizations of uniform global exponential stability (UGES) and uniform global asymptotic stability (UGAS) of arbitrary closed (not necessarily compact) sets for nonlinear difference inclusions. In particular, we provide several characterizations of these stability properties via summability criteria that do not require the knowledge of a Lyapunov function. We...

This paper is concerned with stability analysis for singular systems with interval time-varying delay. By constructing a novel Lyapunov functional combined with reciprocally convex approach and linear matrix inequality LMI technique, improved delay-dependent stability criteria for the considered systems to be regular, impulse free, and stable are established. The developed results have advantag...

Westudy conditions underwhich the solutions of a timevarying linear dynamic systemof the formx (t)=A(t)x(t) are stable on certain time scales.We give sufficient conditions for various types of stability, including Lyapunov-type stability criteria and eigenvalue conditions on “slowly varying” systems that ensure exponential stability. Finally, perturbations of the unforced system are investigate...

This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM...