Topological equivalence of linear time-varying control systems

Abstract

Abstract In this paper, we mainly studied the topological equivalence of linear time-varying (LTV) control system $\dot{x}\left ( t\right )=A(t)x(t)+B(t)u(t)$ defined on an interval $I \subset \mathbb{R}^{+}$. After giving a new definition of the topological equivalence, we investigated the local equivalence of LTV control systems under two new hypotheses. These hypotheses were made by the local behavior of Krylov indices (which turned out to be controllability indices for the linear time-invariant (LTI) control systems). It was found out that Krylov indices play an important role in the classification problem of LTV control systems. Compared with our former work on the topological equivalence of LTI control systems, new methods and techniques were taken to deal with new difficulties occurred for LTV control systems.