On the nonresonance property of linear differential-algebraic systems (Q414046)

A system of linear ordinary differential equations in which the coefficient matrix multiplying the derivative of the unknown vector function is identically singular is considered. For systems with constant and variable coefficients, a nonresonance criterion (criterion for bounded-input bounded-output stability) is obtained. For single-input control systems, the problem of synthesizing a nonresonant system in the stationary and nonstationary cases is investigated. An arbitrarily high unsolvabitity index is admitted. The analysis is carried out under assumptions providing the existence of a so-called ``equivalent form'' with separated ``algebraic'' and ``differential'' components.