Robust stabilization design for nonlinear stochastic system with Poisson noise via fuzzy interpolation method

Because the noise for a real dynamical system may be Poisson process due to discontinuous random fluctuation, the H∞ robust control designs for nonlinear stochastic systems with external disturbance and Poisson noise are studied. The H∞ robust control designs need to solve Hamilton–Jacobi inequality (HJI) for these nonlinear stochastic systems to efficiently attenuate the effect of the external disturbance and Poisson noise. Since it is difficult to solve the HJI directly, the fuzzy approach is developed to simplify the design procedure of the H∞ robust control designs for nonlinear stochastic systems with external disturbance and Poisson noise. The asymptotic stability in probability of the proposed nonlinear stochastic control systems under disturbance free condition is also discussed. If the system state variables are unavailable, then the H∞ robust estimator-based output feedback control design is also proposed for nonlinear stochastic systems with external disturbance and Poisson noise. Finally, an example of robust control of nervous system with Poisson stimulation in Parkinsonism patients is given to confirm the performance of the proposed method.