A necessary and sufficient condition as well as a sufficient condition of asymptotic stability for interval symmetric matrices (Q1919016)

For symmetric \(n\times n\) interval matrices \(G[B, C]= \{A|A= (a_{ij})=A^T, b_{ij}\leq a_{ij}\leq c_{ij}\}\), \(B= (b_{ij})= B^T\), \(C= (c_{ij})= C^T\), the author obtains conditions for asymptotical stability which use a reduced comparison set \(K[B, C]= \{\widetilde A|\widetilde A= (C+ B)/2+ \text{diag}(\delta_1, \dots, \delta_n) (C- B)/2\text{ diag}(\delta_1,\dots, \delta_n)\}\), where \(\delta_i= \pm 1\) \((i= 1,\dots, n)\), and so are weaker than the stability conditions known up to now [see e.g. \textit{M. Mansour}, Int. J. Control 47, No. 6, 1973-1974 (1988; Zbl 0648.15006)]. The proofs use Lyapunov functions.