Abstract This manuscript is involved in the study of stability solutions functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on different types random/stochastic systems, specifically, delay (SDDEs). Introducing appropriate Lyapunov functionals enables us to investigate necessary conditions for stability, asymptotic mean square exponential global ...

This paper studies contraction analysis of switched systems that are composed a mixture contracting and noncontracting modes. The first result pertains to the equivalence system uniform global exponential stability its variational system. Based on this property, sufficient conditions for mode-dependent average dwell/leave-time based switching law be contractive established. Correspondingly, LMI...

In this paper we show that uniformly global asymptotic stability for a family of ordinary diierential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H 1 estimate.

The dynamical stability of planar networks of non-uniform Timoshenko beams system is considered. Suppose that the displacement and rotational angle is continuous at the common vertex of this network and the bending moment and shear force satisfies Kirchhoff’s laws, respectively. Timedelay terms exist in control inputs at exterior vertices. The feedback control laws are designed to stabilize thi...

In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for input-to-state stability and input-to-state exponential stability, and for input-to-state exponential stability and a nonlinear H∞ estimate.

In this work, we prove the existence of a center manifold for some partial functional differential equations, whose linear part is not necessarily densely defined but satisfies the Hille-Yosida condition. The attractiveness of the center manifold is also shown when the unstable space is reduced to zero. We prove that the flow on the center manifold is completely determined by an ordinary differ...

We analyze the Markov–Bernstein type inequalities between norms of functions and their derivatives for complex exponential polynomials. establish a relation sharp constants in these stability problem linear switching systems. In particular, maximal discretization step is estimated. prove monotonicity with respect to exponents, provided those exponents are real. This gives asymptotically tight u...

This paper is concerned with the numerical approximation by compact finitedifference schemes of differential operators of the form Leu = eu(m) + ^Jv=0 avv^ without turning points. The stability of L£ combined with various auxiliary conditions is discussed, and a representation result for solutions of problems involving it is proven. This representation decomposes the solution into a smooth oute...

This paper proves that the stability region of a 2-station, 5-class reentrant queueing network, operating under a non-preemptive static buffer priority service policy, depends on the distributions of the interarrival and service times. In particular, our result shows that conditions on the mean interarrival and service times are not enough to determine the stability of a queueing network, under...