We study solutions of almost periodic linear differential systems. This field is called the Favard theory what is based on the famous Favard result in [10] (see, e.g., [3, Theorem 1.2] or [28, Theorem 1]). It is a well-known corollary of the Favard (and the Floquet) theory that any bounded solution of a periodic linear differential system is almost periodic (see [12, Corollary 6.5] and [13] for...

We investigate pattern formation in two-dimensional anisotropic systems under an external spatially periodic modulation force. Electrohydrodynamic convection or RayleighB6nard convection of nematic liquid crystals are typical examples of anisotropic pattern forming systems. We are especially interested in the situation where the wave vector of the convection rolls and the wave vector of the ext...

In this paper, the problem of input reconstruction for the general case of periodic linear systems driven by periodic inputs ẋ = A(t)x + A0(t)w(t), y = C(t)x is addressed where x(t) ∈ Rn and A(t), A0(t), and C(t) are T0-periodic matrices and w is a periodic signal containing an infinite number of harmonics. The contribution of this paper is the design of a real-time observer of the periodic exc...

In this paper, we consider periodic linear systems driven by T0-periodic signals that we desire to reconstruct. The systems under consideration are of the form ẋ=A(t)x+A0(t)w(t), y=C(t)x, x ∈ Rn, w ∈ Rm, y ∈ Rp , (m p n) where A(t), A0(t), and C(t) are T0-periodic matrices. The period T0 is known. The T0-periodic input signal w(t) is unknown but is assumed to admit a finite dimensional Fourier ...

This paper deals with the automated veriication of a class of task-control systems with periods, durations, and scheduling specii-cations. Such systems are translated into Periodic Hybrid Automata for veriication. We show that safety, liveness, and time-bounded properties are decidable for the considered systems.

This paper is concernedwith a periodic system dependent on parameter. We study differentiability with respect to parameters of the periodic solution of the system. Applying a fixed point theorem and the results regarding parameters for C0-semigroups, we obtained some convenient conditions for determining differentiability with parameters of the periodic solution. The paper is concluded with an ...

A specification of the linear system theory over dioids is proposed for periodic systems. Using the conventional periodic system theory as a guideline, we study periodic systems for which the underlying algebraic structure is a dioid. The focus is on representations (impulse response and state model) associated with such systems, the properties of these representations as well as the state spac...

When standard alphabets are used with monoalphabetic systems, three approaches are possible. The simplest occurs when text can be immediately identified. Identification of only two or three letters in a standard unilateral alphabet is sufficient to reconstruct and confirm the entire alphabet. The other two methods, where text is not readily identifiable, are to match frequency patterns to the n...

In this paper we consider a class of planar autonomous systems having an isolated limit cycle x0 of smallest period T > 0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order...

Reasonable sufficient conditions are obtained for the existence of positive periodic solutions in periodic delayed Gause-type predator-prey systems. Our approach involves the application of coincidence degree theorem and estimations of uniform upper bounds on solutions. This method imposes minimum restrictions on the form and magnitude of time delays. Indeed, our results are applicable to discr...