Asynchronous Spectrum Assignment for Linear Almost Periodic Systems with Diagonal Mean of the Coefficient Matrix
А. К. Деменчук · Differential Equations · 2021
Abstract We consider a linear control system with an almost periodic coefficient matrix whose mean is a diagonal matrix and with a linear state feedback control. The control matrix is a constant square matrix and has zero rows, and its nonzero rows are linearly independent. The feedback gain is assumed to be almost periodic and such that its frequency module is contained in the frequency module of the coefficient matrix. Necessary and sufficient conditions under which the asynchronous spectrum assignment problem is solvable for this system are obtained. The problem is to find a feasible control such that the closed-loop system has almost periodic solutions with prescribed frequencies, the intersection of the frequency modules of the solution and the coefficient matrix being trivial.