The prediction of epileptic seizure, like the disease itself, is a very old but largely unresolved problem. The prediction may highly improve the quality of life for an epileptic patient. A low cost measurement like Electroencephalogram (EEG) involves the non-invasive monitoring of the brain voltage signals to detect the epileptic seizure. This work aims at finding ways to estimate the internal states of the neuron population by looking at the measured EEG signals so that the seizure onset may be predicted in advance. If one may estimate the states of the neural population, then by relating to the bifurcation horizon, one may find the seizure onset time. To find such states one need an estimator/observer of a neuronal state space model. Most of the neuronal models, be it biological or phenomenological, are nonlinear. If a linear or any other approximation is used for the observer design, the bifurcation horizon may not be accurate enough. The biological models of neural population have the barrier of determining all the physiological parameters of a patient which may be bit limiting. Phenomenological neuron model like Epileptor is adapted, which is a nonlinear and discontinuous model, estimating its states may help in finding the bifurcation parameters. However, the nonlinearities are of Lipschitz and monotonic class. Using Linear Matrix Inequality solutions, a Lipschitz Nonlinear model based Observer is developed and tested in simulation, without using approximations of any kind. The simulation shows high fidelity of the observer to the model at hand estimating the states helping in determining the bifurcation parameters.
