M. de la Sen (Spain)
α-Stability, spectrum assignment, stable matrices, time-delay systems
The asymptotic stability of time delayed systems subject to multiple bounded point delays has received important attention in the last years (see, for instance [1-5]). It is basically proved that the -stability locally in the delays (i.e. all the eigenvalues have prefixed strictly negative real parts located in Re s † - α< 0) may be tested for a set of admissible delays including possible zero delays either through a set of Lyapunov's matrix inequalities or, equivalently, by checking that an identical number of matrices related to the delayed dynamics are all stability matrices. The result may be easily extended to check the -asymptotic stability independent of the delays, i.e., for all the delays having any values, the eigenvalues are stable and located in Re s † ε →0 -, [1] , [3]. The above referred number is 2^r for a set of distinct r point delays and includes all possible cases of alternate signs for summations for all the matrices of delayed dynamics, [3]. The manuscript is completed with a study for prescribed pole-placement (or spectrum assignment) under output feedback.
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