New results on discrete-time bounded real lemma for singular systems: strict matrix inequality conditions

Some existing bounded real conditions for discrete-time singular systems usually include a semi-definite matrix inequality which can not be solved by standard LMI solvers. In this paper we prove that the semi-definiteness constrain may be removed and the corresponding bounded real lemma can be described by a strict matrix inequality. The results lead to more tractable and reliable computation when applying them to design control systems.