On an algorithm for construction a piecewise constant control for a continuous Roesser system construction read constructing

摘要

We consider a linear Roesser system which is a continuous version of discrete Roesser system. In the paper (Idczak and Majewski) it was proved that the attainable set for a continuous Roesser system corresponding to piecewise constant controls is dense in the attainable set corresponding to integrable controls. Similar result was proved for the class of Goursat-Darboux system (Idczak and Walczak, 2004). Moreover in the paper (Idczak and Majewski) the authors gave a general algorithm for finding a piecewise constant control connected with mentioned density result for a Goursat-Darboux system. The algorithm is based on the proof of the Baciotti-Sentis lemma. In this paper we show how one can use this algorithm for finding a piecewise constant control for the class of Roesser systems. We also present an example of using this algorithm for concrete problem.