In this paper we consider a modification of a criterion of the exponential stability for the linear system with a single delay. This criterion requires checking for positive definiteness of some block matrix which is based on the fundamental matrix of the system and on the Lyapunov matrix. The dimension of this block matrix depends on the matrices of the system and the delay value, and it can be very large. The purpose of our work is to reduce the dimension. To solve this problem, we use an improved approximation of functions from a given relatively compact set by functions of a special form due to a more rational choice of discretizing points. As a result, we reduced the dimension of the block matrix by almost half.
|Journal||ПРОЦЕССЫ УПРАВЛЕНИЯ И УСТОЙЧИВОСТЬ|
|State||Published - 2020|
- exponential stability
- Linear time-delay system
- линейная система с запаздывание
- экспоненциальная устойчивость