Stability tests for two common 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 due to the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. 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