Almost periodic solutions of differential equations with piecewise constant argument of generalized type

We consider the existence and stability of an almost periodic solution of the following hybrid system:


Periodic solutions of the hybrid system with small parameter
Akhmet, Marat; Ergenc, T. (Elsevier BV, 2008-06-01)
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.
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...
Exhaustive study on the commutativity of time-varying systems
KÖKSAL, MUHAMMET (Informa UK Limited, 1988-5)
This paper, which is a survey and a compact reference on the commutativity of time-varying systems, gives the complete set of necessary and sufficient commutativity conditions for systems of any order. Original results are derived on Euler's systems, and explicit commutativity conditions are presented for fourth-order systems, which have not yet appeared in the literature.
Growth rate of switched homogeneous systems
Tuna, Sezai Emre (Elsevier BV, 2008-11-01)
We consider discrete-time homogeneous systems under arbitrary switching and study their growth rate, the analogue of joint spectral radius for switched linear systems. We show that a system is asymptotically stable if and only if its growth rate is less than unity. We also provide an approximation algorithm to compute growth rate with arbitrary accuracy.
Exact solutions of the modified Kratzer potential plus ring-shaped potential in the d-dimensional Schrodinger equation by the Nikiforov-Uvarov method
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-02-01)
We present analytically the exact energy bound-states solutions of the Schrodinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov-Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.
Citation Formats
M. Akhmet, “Almost periodic solutions of differential equations with piecewise constant argument of generalized type,” NONLINEAR ANALYSIS-HYBRID SYSTEMS, pp. 456–467, 2008, Accessed: 00, 2020. [Online]. Available: