International Journal of Bifurcation and Chaos · 1996 · 18 citations · 0 references
Natural SciencesMathematicsComplex SystemsDynamical SystemsSystem DynamicsChaos TheoryControl Of Dynamical SystemsControl TheoryFixed PointsNonlinear ControlStabilityChaotic DynamicsDynamical Systems StabilityLinear ControlLinear Control SystemsNonlinear StabilityNonlinear Stability AnalysisStability MarginsStability Of Fixed Points
In this paper, conditions for effective local control of nonlinear, chaotic dynamical systems are analyzed. The aim is to determine the size of a neighbourhood of a fixed point in which the system remains stable when subjected to a linear control law. The stability margins are obtained using ideas from functional analysis, and ways of implementing the obtained results in practice are proposed. An implementation of obtained conditions is illustrated on a real application.