Invariants of linear control systems with analytic matrices and the linearizability problem

TL;DR

This paper investigates the invariants of linear control systems with analytic matrices and develops criteria for when nonlinear control systems can be transformed into linear ones, generalizing previous results and connecting to differential equations with meromorphic coefficients.

Contribution

It provides a comprehensive description of invariants for non-autonomous linear systems with analytic matrices and establishes new conditions for their linearizability without specifying a target system.

Findings

Derived invariants classify linear systems up to coordinate transformations.

Established a criterion for mapping nonlinear systems to linear systems with analytic matrices.

Connected the problem to linear differential equations with meromorphic coefficients.

Abstract

The paper continues the authors' study of the linearizability problem for nonlinear control systems. In the recent work [K. Sklyar, Systems Control Lett. 134 (2019), 104572], conditions on mappability of a nonlinear control system to a preassigned linear system with analytic matrices were obtained. In the present paper we solve more general problem on linearizability conditions without indicating a target linear system. To this end, we give a description of invariants for linear non-autonomous single-input controllable systems with analytic matrices, which allow classifying such systems up to transformations of coordinates. This study leads to one problem from the theory of linear ordinary differential equations with meromorphic coefficients. As a result, we obtain a criterion for mappability of nonlinear control systems to linear control systems with analytic matrices.