摘要：AbstractThis paper deals with the stability analysis of time delay systems based on continuous-time approach. The originality of the present paper relies on the construction of several models for a same time-delay systems using the interconnection of an ordinary differential equation and a transport partial differential equation. The stability analysis is then performed using a Lyapunov functional. These models are constructed in order to first reduce potentially the complexity of the resulting stability conditions. Second several models are build in order to be interpreted as a discretization scheme as the one usually used in the Lyapunov functional. The proposed result can be seen as a generalized(N — M)discretization which consists in both a time-discretization of the delay interval intoMsub-intervals, and the projection of the state function within each sub-interval on the Legendre polynomials of degree less thanN.The efficiency of this novel approach is illustrated on an academic example.
