Abstract: It is known that the asymptotical stability of the
linear time invariant descriptor system is related to the solution of the
generalized Lyapunov equation If E
is singular, the generalized Lyapunov equation may have no solution even if all
the finite eigenvalues of have a negative real part, and a
solution, if it does exist, is not unique. This paper attempts to introduce a
matrix G through which to introduce a
standard Lyapunov equation, and then proves a relation between the asymptotical
stability of the linear time invariant descriptor system with E
singular and the solution of the standard Lyapunov equation. Meanwhile, the
matrix G would be described as a contour integral and in terms of the
coefficient of Laurent series of at infinity.
Keywords and phrases: descriptor system, matrix pencil, Weierstrass canonical normal form, Lyapunov equations.
