Periodic solutions of the hybrid system with small parameter

Akhmet, Marat
Ergenc, T.
In this paper we investigate the existence and stability of the periodic solutions of a quasilinear differential equation with piecewise constant argument. The continuous and differentiable dependence of the solutions on the parameter and the initial value is considered. A new Gronwall-Bellman type lemma is proved. Appropriate examples are constructed.


Almost periodic solutions of differential equations with piecewise constant argument of generalized type
Akhmet, Marat (Elsevier BV, 2008-06-01)
We consider existence and stability of an almost periodic solution of the following hybrid system dx(t) dt = A(t)x(t) + f(t, x(θβ(t)−p1 ), x(θβ(t)−p2 ), . . . , x(θβ(t)−pm )), (1) where x ∈ R n , t ∈ R, β(t) = i if θi ≤ t < θi+1, i = . . .−2, −1, 0, 1, 2, . . . , is an identification function, θi is a strictly ordered sequence of real numbers, unbounded on the left and on the right, pj , j = 1, 2, . . . , m, are fixed integers, and the linear homogeneous system associated with (1) satisfies exponential dich...
Time-constrained temporal logic control of multi-affine systems
Aydın Göl, Ebru (Elsevier BV, 2013-11-01)
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on estimating the time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition syste...
Cyclic codes and reducible additive equations
Guneri, Cem; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2007-02-01)
We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocqu...
Analysis of single Gaussian approximation of Gaussian mixtures in Bayesian filtering applied to mixed multiple-model estimation
Orguner, Umut (Informa UK Limited, 2007-01-01)
This paper examines the effect of the moment-matched single Gaussian approximation, which is made in various multiple-model filtering applications to approximate a Gaussian mixture, on the Bayesian filter performance. The estimation error caused by the approximation is analysed for both the prediction and the measurement updates of a Bayesian filter. An approximate formula is found for the covariance of the error caused by the approximation for a general Gaussian mixture with arbitrary components. The calcu...
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Citation Formats
M. Akhmet and T. Ergenc, “Periodic solutions of the hybrid system with small parameter,” NONLINEAR ANALYSIS-HYBRID SYSTEMS, pp. 532–543, 2008, Accessed: 00, 2020. [Online]. Available: