Accurate stabilization for linear stochastic systems based on region pole assignment and its applications

Abstract

On the premise of ensuring the stability of the closed-loop linear stochastic system, this paper uses region stability to further explore the precise control of its dynamic performance, which is an essential consideration in practical control. First, based on the relationship between the poles (eigenvalues) of the system state matrix and system performance, the sufficient conditions are presented for the distribution of system eigenvalues in the specific convex regions, i.e., a novel criterion for the region stability of the linear stochastic systems. Second, the region stabilization conditions are given by LMIs, which can guarantee that the system eigenvalues distribute in the connected region. Third, a new algorithm is designed to solve the stabilization condition of the eigenvalues of the state matrix located in the unconnected region. Accordingly, some dynamic performance indexes of linear stochastic systems can be controlled more accurately. Finally, two cases are provided to show the precise control for the performance indexes of the new stabilization method. • A new criterion of region stability for linear stochastic systems is presented, which can describe the system performance more accurately. • According to the region stability, a more accurate controller design method is provided, which can not only guarantee the stability of the systems, but also control the dynamic performance of the system accurately. • The convergent speed and damping response of the systems can be controlled effectively by using the region stabilization method.