Generalization of a frequency domain stability criterion for proper linear time-varying systems based on eigenvalue and co-eigenvalue concepts

A time-varying linear dynamical system of the form dx/dt=A(t)x is said to be proper if A(t)=f(t,G), for some (scalar) primitive function f(t, lambda ) and (constant) generating matrix G. In a recent (1987) paper, the authors showed that finite-form analytic solutions and stability information for proper systems dx/dt=A(t)x can be obtained using the conventional (time-varying) eigenvalues of A(t) and novel entities called coeigenvalues of A(t). In particular, a general necessary and sufficient stability criterion of the time-domain type and a restricted stability criterion of the frequency-domain type were developed. The criterion is generalized to extend its domain of application. The result presented can be used to analyze the stability of a broad class of (vector) proper linear time-varying systems.<>