New Quadratic Negative Condition and its Application to the Stability of Time-delayed Linear Systems

In this paper, we consider the stability of time-delayed linear systems. First, based on the segmentation of interval and the S-procedure, we derive a new sufficient condition guaranteeing that a quadratic function is negative for a closed interval. Of course, necessary and sufficient conditions exist, but these are computationally burdensome due to too many additional variables, so sufficient conditions with few variables are required. Next, we choose an LKF and find the upper bound of its time derivative along the trajectories of systems. To transform it into the form of LMI, we apply the Bessel-Legendre inequality, the reciprocally convex inequality, and derived quadratic negative condition. Finally, two well-known numerical examples are provided to show that the proposed results are valid and less conservative. Copyright © The Korean Institute of Electrical Engineers.