Stability results for two classes of linear time-delay and hybrid systems

The stability of linear time-delay systems with point internal delays is difficult to deal with in practice because of the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. This feature causes usually the system to possess an infinite number of poles. In this paper, stability tests for this class of systems are obtained either based on extensions of classical tests applicable to delay-free systems or on approaches within the framework of two-dimensional digital filters. Some of those two-dimensional stability tests are also proved to be useful for stability testing of a common class of linear hybrid systems which involve coupled continuous and digital substates after a slight "ad-hoc" adaptation of the tests for that situation.