Multiplicity-Induced-Dominancy extended to neutral delay equations: Towards a systematic PID tuning based on Rightmost root assignment

International audienceRecently, the conditions on a multiple spectral value to be dominant for retarded time-delay system with a single delay were deeply explored. Such a property was called Multiplicity-Induced-Dominancy. It was then exploited in the design of delayed stabilizing controllers. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates' delays and gains result from the manifold defining the maximal multiplicity of a real spectral value. This can also be seen as a pole-placement method, which unlike methods based on finite spectrum assignment does not render the closed loop system finite dimensional but consists in controlling its rightmost spectral value. This work aims at extending such a design approach to time-delay systems of neutral type occurring in the classical problem of PID stabilizing design for delayed plants. More precisely, the controller's gains (ki, kp, k d) are tuned using the intentional multiplicity's algebraic constraints allowing to the stabilization of unstable delayed plants. The specificity, of such a design is related to the analytical assignment of the closed-loop solution's decay rate