Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations

Lyapunov and exponential dichotomy spectral theory is extended from ordinary differential equations (ODEs) to nonautonomous differential-algebraic equations (DAEs). By using orthogonal changes of variables, the original DAE system is transformed into appropriate condensed forms, for which concepts such as Lyapunov exponents, Bohl exponents, exponential dichotomy and spectral intervals of various kinds can be analyzed via the resulting underlying ODE. Some essential differences between the spectral theory for ODEs and that for DAEs are pointed out. It is also discussed how numerical methods for computing the spectral intervals associated with Lyapunov and Sacker-Sell (exponential dichotomy) can be extended from those methods proposed for ODEs. Some numerical examples are presented to illustrate the theoretical results.