相关论文: A remark on the converging-input converging-state …

This note provides a general construction, and gives a concrete example of, forced ordinary differential equation systems that have these two properties: (a) for each constant input u, all solutions converge to a steady state but (b) for…

The transition from a non-equilibrium state to an equilibrium state is characterized not only by the disappearance of the entropy production, but mainly by the disappearance of the organized currents, due to the gradients present in a…

The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…

This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring…

We develop an asymptotical control theory for one of the simplest distributed oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of string states that admit…

Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this…

Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…

The problem of state-feedback stabilizability of discrete-time nonlinear systems has been considered in this note. Two assertions have been proved. First, if the system is $N$-step controllable to the origin, then there is a state feedback…

Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…

Various formulations of counterfactual general equilibrium in economies -- systems of actors manipulating economic goods -- are logically and mathematically analyzed. Evenly-rotating economies are systems whose evolution is stable, steady,…

A physical system is called quasi-isolated if it subject to small random uncontrollable perturbations. Such a system is, in general, stochastically unstable. Moreover, its phase-space volume at asymptotically large time expands. This can be…

For transitive shifts of finite type, and more generally for shifts with specification, it is well-known that every equilibrium state for a Holder continuous potential has positive entropy as long as the shift has positive topological…

The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with…

The principles of static equilibrium are of special interest to civil engineers. For a rigid body to be in static equilibrium the condition is that net force and net torque acting on the body should be zero. That clearly signifies that if…

This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…

Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…

In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the…

A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…

Passivity is an imperative concept and a widely utilized tool in the analysis and control of interconnected systems. It naturally arises in the modelling of physical systems involving passive elements and dynamics. While many theorems on…

The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds…