Stability of Motion

addition apply arbitrarily assume asymptotically stable autonomous becomes behavior belongs boundary bounded called characteristic roots choose closed coefficients components condition consider constant construct contains continuous converges corresponds curve defined denote depends derivative determined differential equation equal equilibrium estimate example exists expression finite fixed follows further given Hence hypothesis implies increases inequality initial values instance integral interval introduce least Liapunov function linear matrix means method motion negative obtain origin parameter partial periodic solution phase polynomial positive definite possible problem proof properties resp respect right side satisfies scalar sequence singular point space stability sufficiently t₁ tends Theorem tion trajectory transfer transformation uniformly unit unstable valid values variable vector zero