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Sufficiency-Type Stability and Stabilization Criteria for Linear Time-Invariant Systems with Constant Point Delays
Authors:M De La Sen
Institution:(1) Instituto de Investigación y Desarrollo de Procesos IIDP, Facultad de Ciencias, Universidad del País Vasco, Leioa (Bizkaia), Aptdo. 644 de Bilbao, 48080-Bilbao, Spain
Abstract:A set of criteria of asymptotic stability for linear and time-invariant systems with constant point delays are derived. The criteria are concerned with agr-stability local in the delays and epsi-stability independent of the delays, namely, stability with all the characteristic roots in Rethinspsleagr<0 for all delays in some defined real intervals including zero and stability with characteristic roots in Rethinsps<–epsi<0 as epsirarr0+ for all possible values of the delays, respectively. The results are classified in several groups according to the technique dealt with. The used techniques include both Lyapunov's matrix inequalities and equalities and Gerschgorin's circle theorem. The Lyapunov's inequalities are guaranteed if a set of matrices, built from the matrices of undelayed and delayed dynamics, are stability matrices. Some extensions to robust stability of the above results are also discussed.
Keywords:point delays  Lyapunov stability  stability and closed-loop stabilization  time-delay systems
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