查看更多>>摘要：The problem of delayed input control for a nonlinear system is discussed, where the nonlinearities of nonlinear systems are not assumed as Lipschitz continuous, they can be non Lipschitz continuous or discontinuous in this paper. Notice that as a general nonlinear system, its sub-systems may have no common equilibrium or no equilibriums, but their trajectories may still be kept near equilibriums. Motivated by this, practical stability of nonlinear systems is considered by employing the Lyapuov method. Practical stability criteria in forms of linear matrix inequalities are obtained, where improved integral inequalities are given to reduce the conservatism of the obtained results. Finally, the obtained results are applied to analyze two problems of load frequency control of a one-area networked power system with sampled input and flight control of a two-degree-freedom helicopter system. The advantage and effectiveness of our approach are shown by a comparison with the literature. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let G be a graph. For a subset X of V(G), the switching sigma of G is the signed graph G(sigma) obtained from G by reversing the signs of all edges between X and V(G) \ X. Let A(G(sigma)) be the adjacency matrix of G(sigma). An eigenvalue of A(G(sigma)) is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let S-n,S-k be the graph obtained from the complete graph Kn-r by attaching r pendent edges at some vertex of Kn-r. In this paper we prove that there exists a switching sigma such that all eigenvalues of G(sigma) are main when G is a complete multipartite graph, or G is a harmonic tree, or G is a S-n,S-k. These results partly confirm a conjecture of Akbari et al. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let m , n , h and k be four integers with 1 & LE; h & LE; m and 1 & LE; k & LE; n , and let U and W be two mutually disjoint nonempty vertex sets with | U| = m and | W | = n . An [ h, k ]-bipartite hypertournament BT with vertex sets U and W is a triple (U, W ; A(BT)), where A(BT) is a set of (h + k )-subset of U boolean OR W , called arcs with exactly h vertices from U and exactly k vertices from W , such that for any (h + k )-subset U 1 boolean OR W 1 of U boolean OR W , A(BT) contains exactly one of the (h + k ) ! (h + k)-tuples whose entries belong to U 1 boolean OR W 1 . In this paper, we prove that every [ h, k ]-bipartite hypertournament with m + n vertices, where 2 & LE; h & LE; m - 1 and 2 & LE; k & LE; n - 1 , has a hamiltonian path. (c) 2022 Elsevier Inc. All rights reserved.
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