Brief paper: Strict linear matrix inequality characterisation of positive realness for linear discrete-time descriptor systems

Positive realness is an important concept in control theory. For linear discrete-time descriptor systems, the positive realness lemma involves non-strict linear matrix inequality (LMI) and may cause numerical problems in practice. Here, strict LMI characterisation for positive realness for linear discrete-time descriptor systems is established. The new characterisation can be efficiently solved by the standard LMI toolbox and may take important functions in related design problems.