An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay

The reciprocally convex combination lemma (RCCL) is an important technique to develop stability criteria for the systems with a time-varying delay. This note develops an extended reciprocally convex matrix inequality, which reduces the estimation gap of the RCCL-based matrix inequality and reduces the number of decision variables of the recently proposed delay-dependent RCCL. A stability criterion of a linear time-delay system is established through the proposed matrix inequality. Finally, a numerical example is given to demonstrate the advantage of the proposed method.