Fast-Lifting Approach to the Computation of the Spectral Radius of Neutral Time-Delay Systems

This paper discusses a further development of the lifting-based method for continuous-time time-delay systems (TDSs), in which the state transition is viewed in discrete-time and described by the monodromy operator. The method deals with only infinite-dimensional bounded operators without taking any process that directly reduces the infinite-dimensionality to finite-dimensionality, and only uses “pseudo-discretization” induced by the fast-lifting technique. A key role of fast-lifting lies in facilitating an appropriate approximation of the monodromy operator with a tractable one that is still infinite-dimensional, where the latter eventually leads to the reduction to finite-dimensionality. The method is thus purely operator-theoretic and also system-theoretic. Under such a framework, a finite-dimensional computation method of the spectrum of the monodromy operator was derived in a preceding paper, which is ensured to be asymptotically exact as the fast-lifting parameter N tends to infinity but was restricted to retarded time-delay systems. This paper shows that a similar method can be established also for neutral TDSs as far as the spectral radius computation is concerned.