In this paper we develop Lyapunov and invariant set stability theorems for non-linear impulsive dynamical systems. Furthermore, we generalize dissipativity theory to non-linear dynamical systems with impulsive e€ ects. Speci®cally, the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpre...

We propose an abstract framework for the computation of the spectrum (A) of a linear operator A : D(A) X ! X on a Banach space X through a condition in a smaller Banach space X 1. If this space is nite dimensional this yields a characteristic equation for (A). The method is tested for delay, integro-diierential and population equations and is applicable to control and stability questions. The s...

This paper introduces stabilization techniques for intrinsically unstable, high accuracy rational approximation methods for strongly continuous semigroup. The methods not only stabilize the approximations, but improve their speed of convergence by a magnitude of up to 1/2.

We discuss conditions such that strong stability and strong asymptotic compactness of a (discrete or continuous) semiflow defined on a subset in the positive cone of an ordered Banach space is preserved under asymptotic domination. This is used to show that on a Banach lattice with order continuous norm strong stability and almost periodicity of a (discrete or strongly continuous) semigroup of ...

For Markov processes with absorption, we provide general criteria ensuring the existence and exponential non-uniform convergence in weighted total variation norm to a quasi-stationary distribution. We also characterize subset of its domain attraction by an integrability condition, prove right eigenvector for semigroup process ergodicity Q-process. These results are applied one-dimensional multi...

We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-v...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

We consider a very simple Mealy machine (two non-trivial states over a two-symbol alphabet), and derive some properties of the semigroup it generates. It is an infinite, finitely generated semigroup, and we show that the growth function of its balls behaves asymptotically like nα, for α = 1 + log 2/log 1+ √ 5 2 ; that the semigroup satisfies the identity g = g; and that its lattice of two-sided...