Recent investigations have shown that with systemic parameters falling into a certain area a power system undergoes subcritical and supercritical Hopf, saddle-node, and period-doubling bifurcations which severely threaten the secure and stable operation of power system, even to the point of inducing voltage collapse. To control these undesirable bifurcations, an adaptive control law is presented based on the LaSalle invariance principle, which can asymptotically stabilize an unstable power system to equilibrium points. The control technique does not require analytical knowledge of the system dynamics and operates without explicit knowledge of the desired steady-state position. Simulation results show that the proposed control law is very effective. The research of this paper may help to maintain the power system's security operation.

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A new control law is proposed to asymptotically stabilize the chaotic neuron system based on LaSalle invariant principle. The control technique does not require analytical knowledge of the system dynamics and operates without an explicit knowledge of the desired steady-state position. The well-known modified Hodgkin-Huxley (MHH) and Hindmarsh-Rose (HR) model neurons are taken as examples to verify the implementation of our method. Simulation results show the proposed control law is effective. The outcome of this study is significant since it is helpful to understand the learning process of a human brain towards the information processing, memory and abnormal discharge of the brain neurons.

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