Simple adaptive PI control for linear time-delay systems

A simple direct adaptive proportional-plus-integral (PI) control scheme is introduced, for linear time-delay systems with polytopic uncertainties. Sufficient conditions for closed-loop stability of the proposed control scheme are given, in terms of bilinear matrix inequalities (BMIs). The addition of a proportional-gain feedback to previous results, where only integral-type gain adaptation was considered, reduces the conservatism entailed in the BMIs. Stability is analyzed using the Lyapunov-Krasovskii functional method and both delay-dependent and delay-independent results are obtain. A numerical example is given, which demonstrates applicability of the proposed method and the simplicity of its implementation.