Delay-dependent robust stability and stabilization for systems with mismatched uncertainties

The problems of robust stability analysis and robust feedback synthesis for a class of linear dynamical systems with constant time delay and mismatched uncertainties are considered. This paper develops methods for robust stability and stabilization, which depend on the size of the delay and is conveniently expressed in the form of linear matrix inequalities (LMIs) for which there exist flexible and computationally efficient algorithms. Several standing results are extracted as special cases. The problem of determining upper bounds for the time delay which ensure either robust stability or robust stabilization can be easily solved using the developed LMI formalism.