On the continuity of the speed function of a linear system in the critical case
The paper deals with the dynamic object described by the linear differential equation \[ \dot z= F(z,\nu), \qquad (z,\nu)\in \mathbb{R}^n \times V_0. \] Given the quality functional \[ J(\omega (\cdot))= \lim_{\alpha\to \infty} {1\over {2\alpha}} \int^\alpha_{-\alpha} g(z (t),\nu(t)) dt \] where the control \(\nu: \mathbb{R}^1\to V_0\) is a measurable and periodic function in a compact set \(V_0 \subset \mathbb{R}^m\), the main purpose of the paper is to minimize the functional \(J\). The text is badly organized and the English is poor and incorrect. Moreover, taking into account that the problem does not contain new theoretical elements, one should state that the paper is rather little useful.
scientific article; zbMATH DE number 815650