Stability of linear differential-algebraic systems
Linear differential-algebraic equations (DAEs) \[ A(t)x'(t)+B(t)x(t)=f(t) \] are addressed in this paper using left-regularizing operators. The authors remark that for sufficiently smooth coefficients \(A\) and \(B\), the existence of such a left-regularizing operator is equivalent to the existence of a Cauchy-type general solution and for analytic cases, to the existence of a standard canonical form. Within this framework, they obtain Lyapunov stability criteria and prove an analog of Floquet's theorem leading to stability results for periodic homogeneous DAEs.
scientific article; zbMATH DE number 2170209