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On the state space realization of 2D (2,2)-periodic image behaviors

Publication . Aleixo, José; Napp, Diego; Pereira, Ricardo; Pinto, Raquel; Rocha, Paula

In this paper we consider 2D behaviors with periodic image representations and provide conditions under which a simple method for obtaining state space realizations by means of 2D periodic (separable) Roesser models can be applied. For the sake of simplicity we restrict our attention to the (2; 2)-periodic case.

2018-07Conference object

Open access

On the state-space realization of 2-periodic image behaviors

Publication . Napp, Diego; Pereira, Ricardo; Pinto, Raquel; Rocha, Paula; Aleixo, José

In this paper we study the realization of periodically time-varying behavioral systems by means of periodic state-space models. In particular, we focus on the case of period two and investigate under which conditions a given behavior with periodic representation obtained by alternating two time-invariant image representations can be realized by a periodic state-space system. We first show that, in general, one cannot expect to obtain a periodic state-space realization by means of the individual realizations of each associated time-invariant behaviors. However, we give conditions for such procedure to hold. The presented results are illustrated by examples.

2018-06Journal article

Open access

Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of integral equations on finite intervals

Publication . Simões, A. M.; Castro, L. P.

The purpose of this work is to study different kinds of stability for a class of integral equations defined on a finite interval. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability by using fixed point techniques and the Bielecki metric.

2017Journal article

Restricted access

Hyers-Ulam-Rassias Stability of Nonlinear Integral Equations Through the Bielecki Metric

Publication . Simões, A. M.; Castro, L. P.

We analyse different kinds of stabilities for classes of nonlinear integral equations of Fredholm and Volterra type. Sufficient conditions are obtained in order to guarantee Hyers‐Ulam‐Rassias, σ‐semi‐Hyers‐Ulam and Hyers‐Ulam stabilities for those integral equations. Finite and infinite intervals are considered as integration domains. Those sufficient conditions are obtained based on the use of fixed point arguments within the framework of the Bielecki metric and its generalizations. The results are illustrated by concrete examples.

2018Journal article

Restricted access

Different Types of Hyers-Ulam-Rassias Stabilities for a Class of Integro-Differential Equations

Publication . Simões, A. M.; Castro, L. P.

We study different kinds of stabilities for a class of very general nonlinear integro-differential equations involving a function which depends on the solutions of the integro-differential equations and on an integral of Volterra type. In particular, we will introduce the notion of {\it semi-Hyers-Ulam-Rassias stability}, which is a type of stability somehow in-between the Hyers-Ulam and Hyers-Ulam-Rassias stabilities. This is considered in a framework of appropriate metric spaces in which sufficient conditions are obtained in view to guarantee Hyers-Ulam-Rassias, semi-Hyers-Ulam-Rassias and Hyers-Ulam stabilities for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Examples of the application of the proposed theory are included.

2017Journal article

Restricted access