D-stability analysis for discrete uncertain time-delay systems

Guaranteed cost D-stabilization and H∞ D-stabilization for linear discrete time-delay systems

“…(4) is less conservative than the criteria proposed in [10] through a numerical example. It is more important that the condition (4) can be used to cope with the problems of Dða,rÞ-stabilization with certain performance requirements.…”

“…This means that the condition jajor is necessary to Lemma 2.1 and Theorem 2.1. For technical reason, the restriction has been shown in almost all results of Dða,rÞ-stability of linear discrete time-delay systems (see for example, [2,10,18,22,26]). It will be a meaningful work to remove the restriction in the future.…”

New Conditions for the Exponential Stability of Nonlinear Differential Equations

“…Bound (27) proves the Lyapunov stability with respect to the ball Ω( ), with = (1 − ( (⋅), )). Now, let < ∞.…”

“…Applying our reasoning above to (30), we get according to inequality (27) that ( ) is a bounded function. Hence (29) yields the exponential stability.…”

“…The stability analysis with respect to a ball has been considered by many researchers (see, e.g., Furuta and Kim [26] and Hsiao et al [27]). However, this kind of stability is defined in terms of the set of roots of characteristic polynomials corresponding to linear autonomous delay equations.…”