Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays |
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| Authors: | Seok Young Lee Won Il Lee PooGyeon Park |
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| Institution: | 1. Division of IT Convergence Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea;2. Department of Electrical Engineering, Pohang University of Science and Technology, Pohang, Republic of Korea |
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| Abstract: | Recently, a polynomials-based integral inequality was proposed by extending the Moon’s inequality into a generic formulation. By imposing certain structures on the slack matrices of this integral inequality, this paper proposes an orthogonal-polynomials-based integral inequality which has lower computational burden than the polynomials-based integral inequality while maintaining the same conservatism. Further, this paper provides notes on relations among recent general integral inequalities constructed with arbitrary degree polynomials. In these notes, it is shown that the proposed integral inequality is superior to the Bessel–Legendre (B–L) inequality and the polynomials-based integral inequality in terms of the conservatism and computational burden, respectively. Moreover, the effectiveness of the proposed method is demonstrated by an illustrative example of stability analysis for systems with additive time-varying delays. |
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| Keywords: | Corresponding author |
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