Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: a predictive approach

In a previous paper (Jia et al. (2002)), several new linear matrix inequality (LMI) conditions have been obtained to reduce the conservativeness for the analysis and the design of continuous-time systems with polytopic-type uncertainty. The results are quite attractive, but their proofs are technical. The aim of this note is to provide a different route to reach the results. To this end, the concepts of standard ε- and λ-blocks are introduced and the corresponding equivalent forms are also defined, based on which the improved representations of given linear matrix inequalities can be predicted by replacing directly the standard blocks with their equivalent forms under two newly established exchange criteria, while the correctness of the predicted results can be tested by the well-known projection lemma.