Improved Lmi Representation for the Analysis of Continuous State Delayed Systems with Polytopic Uncertainty

This paper considers the problem of robust stability for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, new matrix inequalities characterization of delay-dependent robust stability results are exploited, which demonstrat that it allows the use of parameterdependent Lyapunov functions in comparison to the classical one, whose drawback stands in the use of a single Lyapunov function to assess the stability over the whole uncertainty domain. Next, as for delay dependent case, the problem of determining the maximum timedelay under which the system will remain stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.