A Class of Matrix-Valued Function Negative-Determination Method and Its Application to Linear Systems With Time-Varying Delays

Concerning the stability analysis for systems with time-varying delays, a negative-determination method for a class of generalized-convex (generalized-concave) matrix-valued polynomial function is proposed, which is an extension of real-valued quadratic function negative-determination lemma. Initially, the definition of generalized-convex matrix-valued function is presented, and its first-order and second-order determination conditions are established. Subsequently, negative definite sufficient conditions for generalized-convex (generalized-concave) matrix-valued polynomials with high degrees are developed. Further, stability criteria with less conservatism for linear time-delay systems are constructed by applying the proposed method. Finally, a numerical example and a load frequency control example are presented to verify the feasibility and the advantage of the designed method on achieving less conservative stability criterion.