This paper deals with obtaining (necessary and) sufficient conditions for Ψ− uniform asymptotic stability of solutions nonlinear Lyapunov matrix differential equations.

in this paper, global uniform exponential stability of perturbed dynamical systemsis studied by using lyapunov techniques. the system presents a perturbation term which isbounded by an integrable function with the assumption that the nominal system is globallyuniformly exponentially stable. some examples in dimensional two are given to illustrate theapplicability of the main results.

We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Z-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For ...

A nonconservative stability theory for switched linear systems is applied to the convergence analysis of consensus algorithms in the discrete-time domain. It is shown that the uniform-joint-connectedness condition for asymptotic consensus in distributed asynchronous algorithms and multi-particle models is in fact necessary and sufficient for uniform exponential consensus.

In this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations based on rough path analysis; then, we provide the notion of asymptotic stability in roughness to analyze the stability for the systems. In the procedure, we...

The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows on Banach spaces. The obtained results clarify differences between the uniform and nonuniform cases. Some examples are included to illustrate the results.

In this paper we deal with the problem of stability and asymptotic stability of critical points of dynamical polysystems. We obtain results concerning polysystems with and without constraints, by means of uniform families of Liapunov functions. Dynamical polysystems may be interpreted as the topological counterpart of switched systems: our results are compared to those previously obtained in th...

For bilinear infinite-dimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral inputto-state stability. We provide two proofs of this fact. One applies to general systems over Banach spaces. The other is restricted to Hilbert spaces, but is more constructive and results in an explicit form of iISS Lyapunov functions.