On nilpotent singular systems (Q5953954)

The authors deal with basic solution properties of linear nonautonomous differential-algebraic equations of the form NEWLINE\[NEWLINEN(t)\dot z(t)+ z(t)= h(t),\qquad t\in J\subset\mathbb{R}.NEWLINE\]NEWLINE In a first step, sufficient conditions for the existence and uniqueness of solutions in \(J\) are derived. Moreover, in that situation, an explicit representation of the solution \(z(t)\) in terms of functions of \(N(t)\) is given. Finally, a more detailed result is shown if the nilpotency of \(N(t)\) is less equal \(2\).