Journal of Electronics and Control · 1963 · 134 citations · 0 references
Equation XEngineeringSingularly Perturbed ProblemStabilityDiscrete Dynamical SystemMatrix ASystem StabilitySystems EngineeringOscillation TheoryGeometric Singular Perturbation TheoryLinear Control TheoryLinear ControlControl SystemsTrivial Solution
ABSTRACT It is shown that the trivial solution of the equation x'' = A(t)x, where the dash denotes the time derivative, is asymptotically stable if the rate of change of the elements aij(t) of A(t) is sufficiently slow. An explicit bound for the aij(t) is obtained when the matrix A has a special form.