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- On the state-space realization of 2-periodic image behaviorsPublication . Napp, Diego; Pereira, Ricardo; Pinto, Raquel; Rocha, Paula; Aleixo, JoséIn 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.
- On the state space realization of separable periodic 2D systemsPublication . Aleixo, José; Rocha, PaulaThis paper is a preliminary contribution to thestudy of the realization problem for periodic 2D input/output systems. More concretely, separable periodic 2D SISO systems are considered and state space representations by means of separable periodic Roesser models are obtained using suitable invariant formulations.
- Roesser model representation of 2D periodic behaviors: the (2,2)-periodic SISO casePublication . Aleixo, José; Rocha, PaulaIn this paper we consider 2D single-input/singleoutput behaviors described by linear partial difference equations with (2,2)-periodically varying coefficients, and present a method to obtain 2D Roesser state-space representations (or realizations) for such behaviors. Since these cannot be obtained by separately realizing each shift-invariant system resulting from “freezing” the varying coefficients, we propose a method based on the realization of an invariant input/output behavior obtained by suitably “lifting” the trajectories of the original periodic behavior.
- On the state space realization of 2D (2,2)-periodic image behaviorsPublication . Aleixo, José; Napp, Diego; Pereira, Ricardo; Pinto, Raquel; Rocha, PaulaIn 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.