Application of the H Infinity Control Principle to the Sodium Ion Selective Gating Channel on Biological Excitable Membranes

We proposed the infinity control principle to evaluate the Biological function. The H infinity control was applied to the Sodium (Na) ion selective gating channel on the excitable cellular membrane of the neural system. The channel opening, closing and inactivation processes were expressed by movements of three gates and one inactivation blocking particle in the channel pore. The rate constants of the channel state transition were set to be voltage dependent. The temporal changes in amounts per unit membrane area of the channel states were expressed by means of eight differential equations. The biochemical mimetic used to complete the Na ion selective channel was regarded as noise. The control inputs for ejecting the blocking particle with plugging in the channel pore were set for the active transition from inactivated states to a closed or open state. By applying the H infinity control, we computed temporal changes in the channel states, observers, control inputs and the worst case noises. The present paper will be available for evaluating the noise filtering function of the biological signal transmission system.