Stability and stabilization of singular systems: Strict LMI sufficient conditions

This paper discusses strict linear matrix inequalities(LMIs) sufficient condition which can be removed of the equality constraint for linear continuous singular systems. The criteria of stability and stabilization of continuous singular system are presented. The conditions are expressed in terms of strict positive definite LMIs which can reduce the equality constraint and semi-positive definite LMIs and are much more tractable and reliable in numerical computation than existing conditions. The conditions make use of only the system parameter matrices (E, A, B) directly by a restricted equivalent transform without introducing other adjective parameters. A counterexample is given to illustrate the criteria are only a sufficient condition but not are a necessary condition. The idea presented can help to find necessary and sufficient strict LMI criteria without equality constraint conditions of stability and stabilization of continuous singular system.