Lyapunov, Bohl and Sacker-Sell spectral intervals for differential-algebraic equations
The authors extend some classical spectral concepts (Lyapunov, Bohl, Sacker-Sell) that were introduced for ordinary differential equations (ODE), to general linear differential-algebraic equations (DAE) with variable coefficients of the type \[ E(t)x'=A(t)x+f(t) \] on \(I=[0,\infty)\), where \(E,\, A\in C(I,{\mathbb R}^{n\times n})\) and \(f\in C(I,{\mathbb R}^{n})\). The main topics investigated in the present paper include the relations between the spectral characteristics of DAE systems and ODE systems, as well as the stability of the spectra with respect to perturbations arising in the system data. The paper also includes numerical methods for computing the Lyapunov and the Sacker-Sell (exponential dichotomy) spectral intervals. Some open problems are formulated in the last part of this paper.
scientific article; zbMATH DE number 5550493
scientific article