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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.
We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local $w$-uniqueness of the solutions to the linear complementarity problem can be identified by the column competent matrices. We establi
The aim of this paper is to study first order Mean field games subject to a linear controlled dynamics on $mathbb R^{d}$. For this kind of problems, we define Nash equilibria (called Mean Field Games equilibria), as Borel probability measures on the
We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary and suffic
We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear noise of t
Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing app