Orthogonal-polynomials-based integral inequality and its applications to systems with additive time-varying delays

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.     

Multiple graphs clustering by gradient flow method

The core issue of multiple graphs clustering is to find clusters of vertices from graphs such that these clusters are well-separated in each graph and clusters are consistent across different graphs. The problem can be formulated as a multiple orthogonality constrained optimization model which can be shown to be a relaxation of a multiple graphs cut problem. The resulting optimization problem can be solved by a gradient flow iterative method. The convergence of the proposed iterative scheme can be established. Numerical examples are presented to demonstrate the effectiveness of the proposed method for solving multiple graphs clustering problems in terms of clustering accuracy and computational efficiency.