Control design for discrete-time linear systems using extended LMIs with scalar parameters

So-called extended LMIs proved very useful to reduce conservatism in, amongst others, multi-objective control problems for LTI systems, robust analysis problems and robust state feedback design. The extended H2 and H∞ performance characterizations proposed in [2] improved the conditions for multi-objective control that were proposed earlier in [5], and were also extended to reduce conservatism in robust analysis and state feedback design problems [1]. More recently, a more general approach for deriving extended LMIs based on the projection lemma is proposed in [4]. This approach allows to even further reduce conservatism in LMI conditions, by taking into account scalar parameters (see also [3]), summarizing the contribution of this paper.