Section: New Results

Maximal-multiplicity-based rightmost-root assignment for retarded TDS

Participants : Islam Boussaada, Silviu-Iulian Niculescu, Sami Tliba [L2S] , Hakki Unal [Anadolu University] , Toma Vyhlidal [Czech Technical University] .

The proposed approach is a stabilizing delayed state-feedback design guaranteeing an appropriate (admissible) convergence rate to the trivial solution of the controlled dynamical system. Unlike methods based on finite spectrum assignment, our method does not render the closed loop system finite dimensional but consists in controlling its rightmost spectral value. First, it consists in characterizing the root of the characteristic quasipolynomial function to be of maximal multiplicity by mean of an analytical necessary and sufficient condition. Then, conditions on such a root (of maximal multiplicity) to be stable and dominant are established. These results are obtained for reduced-orders time-delay system (scalar and quadratic cases), see [69].