A new approach to adaptive impulsive observer design for nonlinear systems

In this paper a new approach is developed for designing adaptive impulsive observers for nonlinear systems with unknown parameters. The basic idea behind the new approach is that an impulsive differential equation is adopted as a model for the desired adaptive impulsive observer, while an impulse-free time-varying differential equation associated with the impulse time sequence is utilized as a model for the parameter estimation law. The designed adaptive impulsive observer is able to estimate both the state and unknown parameters of nonlinear systems. Moreover, the time-varying weighted Lyapunov functions are applied to derive some sufficient conditions for the convergence and stability of the designed adaptive impulsive observer. The effectiveness of the new design approach is validated with the Lorenz system.