On the nonresonance property of linear differential-algebraic systems

We consider a system of linear ordinary differential equations in which the coefficient matrix multiplying the derivative of the unknown vector function is identically singular. For systems with constant and variable coefficients, we obtain nonresonance criteria (criteria for bounded-input bounded-output stability). For single-input control systems, we consider the problem of synthesizing a nonresonant system in the stationary and nonstationary cases. An arbitrarily high unsolvability 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.