‘Output stabilization’ here refers to feedback which drives the system output to 0, without concern for the behavior of the full state. Since everything of concern is automatically observable, it is reasonable to conjecture — subject, of course, to some controllability hypothesis — that this output stabilization should always be possible by some kind of feedback from the output, with no necessity for the usual sort of observability hypothesis. This is true for the finite-dimensional case, but we show, by example, that the conjecture need not hold in infinite-dimensional contexts.
Given a continuous convex function f on a Banach space X, we consider a complete metric space of vector fields V on X with the topology of uniform convergence on bounded subsets. With each such vector field we associate two iterative processes. We show that for a generic V the values of the function f tend to its infimum for both processes.
Classical solutions for nonlinear hyperbolic systems may decay or blow up depending on the damping factors as well as, the size of the initial data. Here we consider a general Cauchy problem and present unified results, which apply to many special cases.
In this paper, we consider a mathematical model of an outbreaks that links the trophic structure of primary and secondary producer in the estuary. Although the environmental and meteorological factors are cosidered to be exogenously induced physical factors that unleashed the bloom, but ensuing duration and severity of an outbreak are largely due to the subsequent biological interplay between organisms. We give results that are qualitatively resemble with those observed in the estuary and thereby offers an insight for the factors that sustain a bloom.
Separatrices in integrable dynamical systems, if perturbed with analytic high frequency perturbations, split apart such that the splitting distance is exponentially small in the frequency parameter omega. This article utilizes a recent straightforward connection between the Melnikov function (which gives a measure of such a splitting) and a Fourier transform, to quantify such splitting under less smooth perturbations. If the perturbation is only piecewise C-k spatially, the splitting distance goes as omega(-k-1) for large omega.
Conditions are obtained for a first order nonlinear differential equation with delay and state dependent impulses to admit a periodic solution of bounded variation. The results are applied to the logistic equation with periodic intrinsic growth rate and periodic impulsive culling.
We prove in this paper that existence and nonoscillation of solutions of some impulsive delayed integrodifferential problem is equivalent to the existence and nonoscillation of solutions of some appropriate integral equation without impulses.
In this note we investigate the behavior of solutions of the difference equationx(n+1) = alpha + beta x(n-1) + gamma x(n-2) + f(x(n-1), x(n-2))/ x(n) n = 0, 1....where alpha, beta, gamma and initial conditions x(-2), x(-1), x(o) are positive real numbers and f : (0, infinity)0)(2) -> (0, infinity) is a real continuous function.
This paper introduces a new transformation method for the mixed H-2/H-infinity. control of a class of uncertain systems. In these systems, there are jumping parameters modelled by a continuous-time, discrete-state Markov process and the uncertainties are assumed to be real, time-varying and norm-bounded. A main portion of the system dynamics is a state-delay with constant delay factor. Through this method, the delay-dependence dynamics is naturally brought up in the design procedure. A state-feedback control is derived for both the nominal and uncertain systems such that the H-2-performance measure is minimized while guaranteeing a prescribed H-infinity-norm bound on the controlled system. All the developed results are cast in the format of linear matrix inequalities (LMIs) and numerical examples are presented.
We develop a nonlinear size-structured phytoplankton-zooplankton aggregation model. We establish a comparison principle and construct monotone sequences to show the existence of a weak solution. We also prove that this solution is unique. As an example, we construct a pair of tipper and lower solutions for a large class of initial data to which all the theory presented applies.
In this paper, we study the existence of positive solutions for a class of semilinear elliptic systems on some classes of unbounded domains.
This work provides sufficient conditions tinder which solutions of a class of nonlinear integrodifferential equations are a priori bounded. The topological transversality theorem is then applied to establish the existence of periodic solutions.
We establish the existence of solutions for a differential equation in Banach spaces. Our analysis relies on two approaches, one using the notion of phi-space together with a fixed point theorem for weakly sequentially continuous maps which are phi-condensing and the other using the Banach contraction principle.
It is shown that mirror symmetric steady states of the evolution of three plane interfaces which move tinder the area preserving curve shortening flow and which meet in one single junction point are exponentially stable with respect to sufficiently small C2+alpha-perturbations.
In this work we study the existence and regularity of mild solutions for a partial second order functional differential equation with impulses.
In this paper we consider a model of a power system which consists of a single electric generator connected to an infinite bus by a transmission line. This model is widely used to study the effect of various controllers on power system stability. In this paper we introduce a smooth nonlinear stabilizing feedback, motivated by so called FACTS devices, which changes the admittance of the transmission line. Our goal is to derive an explicit energy decay estimate for solutions of the corresponding system of ordinary differential equations.
In this paper we consider Lagrange type control problem for systems involving dynamic boundary conditions that is, with boundary operators containing time derivatives. Assuming the existence of optimal controls, B -evolutions theory is used to present necessary conditions of optimality. The result is illustrated by an example from heat transfer problem and also an algorithm for computing optimal controls is presented.
In this note certain notions of asymptotic smoothness and asymptotic compactness are considered, which are suitable to show that, for a continuous map T in a general metric space V, point dissipative implies compact dissipative. Different relations among these mentioned notions are investigated and some weak conditions that lead to compact dissipativeness of T are discussed. Additional remarks concerning alpha-contracting maps are also included.
In this article, we consider the eigenvalue problems of Dirichlet problem -Delta u + u = lambda(f(u) + h(x)) in Omega, u > 0 in Omega, u is an element of H-0(1)(Omega), (*)lambda where lambda > 0, N >= 2, and Omega is an unbounded cylinder domain in R-N. Under some suitable conditions on f and h, we show that there exists a positive constant lambda* such that (*)lambda has at least two solutions if lambda E (0, lambda*), a unique positive solution if lambda = lambda* and no solution if lambda > lambda*. We also obtain some bifurcation results of the solutions at lambda = lambda*.
In this paper we study some properties of the weighted Sobolev space W-sigma(1,p) (R-d, mu) proving in particular that its embedding into the space L-q (R-d, mu) is compact for a certain q < p. From this result we shall deduce the validity of the Poincare inequality for some degenerate Kolmogorov operators of gradient type.
