Improvement of Stability of Time-Delayed Linear Systems via New Constrained Quadratic Matrix Inequality

This paper is concerned with the stability of the linear systems with a time-varying delay. First, we derive a new form of constrained quadratic matrix inequality for the reciprocally convex inequality. Second, an equivalent transform of a constrained quadratic matrix inequality into the form of a linear matrix inequality(LMI) is derived. Third, the upper bound of the time derivative of Lyapunov Krasovskii functional(LKF), in the form of a constrained quadratic matrix, is obtained, and an equivalent transform is done to make it in the form of LMI. Finally, the improvement in stability is shown through two well-known examples.