Stability by Liapunov's Direct Method: With Applications

applications approaches assume asymptotic stability boundary bounded characteristic roots closed cofactors column complete components conclude consider constant continuous coordinates corresponding defined denote determinant diag differential equations discussed distinct energy equilibrium equivalent EXAMPLE existence fact finite escape future given Hence implies important inequality initial inside instance known Lagrange Liapunov function linear matrix means method nonlinear nonsingular obtain origin path periodic positive definite positive solution possible practical stability problem proof quadratic form region relation remain replaced represented require result satisfied scalar shown simple solution space starting sufficiently large Suppose symmetric matrix system F tends Theorem theory tion transformation ultimately unique unstable variable vector written x₁ zero