Further improvement on LMI representations for the analysis and design of continuous-time systems with polytopic type uncertainty

The paper provides a further improvement on a recent result about LMI-based approach for analysis and design of continuous-time systems with polytopic uncertainty. The projection lemma plays a key role in developing the improved LMI-like condition, in which the introduced scalar variable multiplies only with the Lyapunov variable. Roughly speaking, since there is no product term of the introduced scalar variable with system matrices, the derived condition may allow larger uncertainty on system matrices without breaking its feasibility. From another point of view, this helps to find a smaller guaranteed level of attenuation when polytopic type uncertainty is considered. Numerical examples are provided to illustrate the improvement.