This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadraticfunction induced by stability analysis of linear systems with time-varying *** introdu...
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This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadraticfunction induced by stability analysis of linear systems with time-varying *** introducing two adjustable parameters and two free variables,a novel convexfunction greater than or equal to the quadraticfunction is constructed,regardless of the sign of the coefficient in the quadratic *** developed lemma can also be degenerated into the existing quadraticfunction negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular ***,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre *** a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay ***,the superiority of our results is illustrated through three numerical examples.
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