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.


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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...
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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...
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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: