This paper is concerned with the problem of state feedback control for nonlinear quadratic systems with randomly occurring actuator saturation. The considered actuator saturation is assumed to occur in a random way, and the randomly occurring rates of the saturation are time-varying with known upper and lower bounds. By using the Lyapunov approach, a sufficient condition is given to guarantee t...

An adaptive low-gain integral control framework is developed for tracking constant reference signals in a context of nite-dimensional, asymptotically stable, single-input, single-output linear systems subject to locally Lipschitz, monotone input and output nonlinearities of a general nature: the input nonlinearity is required to satisfy an asymptotic growth condition (of suucient generality to ...

It is well-known that the problem of recognizing an ESS in a symmetric bimatrix game is coNPcomplete. In this paper, we show that recognizing an ESS even in doubly symmetric bimatrix games is also coNP-complete. Our result further implies that recognizing asymptotically stable equilibria of the replicator dynamic in this class of games is also a coNP-complete problem. It is also known that a st...

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x(n+1) = x²(n-1)/(ax²(n) + bx(n)x(n-1) + cx²(n-1)), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x₋₁ and x₀ are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilib...

This paper considers how forces are produced by compliance and surface curvature effects in systems where an object B is kinematically immobilized to second-order by finger bodies A1, . . . ,Ak. A class of configuration-space based elastic deformation models is introduced. Using these elastic deformation models, it is shown that any object which is kinematically immobilized to first or second-o...

Two linear feedback control algorithms for handling and preventing congestion in high-speed networks are proposed and analyzed. The fluid approximation model is described with a continuous-time system of delaydifferential equations. The algorithms are asymptotically stable, and the transient processes are nonoscillatory. The control parameters are locally optimal (optimality is based on the asy...

* Correspondence: [email protected] Department of Mathematics and Computer Sciences, Cankaya University, Eskisehir Yolu 29. km, YukariYurtcu Mah. No 80, 06810 Yenimahalle, Ankara, Turkey Full list of author information is available at the end of the article Abstract Our aim in this work is to study the existence and the attractivity of solutions for a system of delay partial integro-differ...

The nonlinear Kuramoto equations for n coupled oscillators are derived and studied. The oscillators are defined to be synchronized when they oscillate at the same frequency and their phases are all equal. A control-theoretic viewpoint reveals that synchronized states of Kuramoto oscillators are locally asymptotically stable if every oscillator is coupled to all others. The problem of synchroniz...

An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to an...

The goal of this article is to provide a construction of a homogeneous Lyapunov function P associated with a system of differential equations J = f(x), x ~ R ~ (n > 1), under the hypotheses: (1) f ~ C(R n, ~ ) vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable. Moreover, the Lyapunov function V(x) tends to infinity with 1[ x [I, and belon...