Quasi-poles of linear time-varying systems in an intrinsic algebraic approach

In a previous piece of work it has been shown that the exponential stability of a linear time-varying (LTV) system can be evaluated using new definitions of the poles of such a system. The latter are given by a fundamental set of roots of the skew polynomial P(partial derivative) which defines the autonomous part of the system. Such a set may not exist over the initial' field K of definition of the coefficients of the system, but can exist over a suitable field extension (K) over tilde superset of K. It is shown here that conditions for stability can also be obtained using linear factors of the polynomial P(partial derivative) over another field extension (sic) which may be smaller: (K) over tilde superset of (sic) superset of K. The roots of these factors are called the quasi-poles of the system. The necessary condition for system stability, expressed in function of these quasi-poles, is more restrictive than the one involving a fundamental set of roots. (c) 2013 Elsevier B.V. All rights reserved.