Adaptive impulsive observers for a class of switched nonlinear systems with unknown parameter

Abstract

This work investigates and solves the design of adaptive impulsive observers for a class of uncertain switched nonlinear systems with unknown parameter. Sufficient conditions are derived for designing such observers for each subsystem to reconstruct asymptotically and update system states in real time. The state observer is represented in terms of impulsive differential equations. The parameter estimation law is modelled by an impulse-free, time-varying differential equation associated with the impulse time sequence in order to determine when the observer estimated state is updated. The asymptotic convergence to zero of the observation errors is established by applying the method of multiple time-varying Lyapunov functions. Sufficient conditions are derived that guarantee the convergence of parameter estimation. An example of switched Lorenz system along with numeric and simulation results is presented to demonstrate the effectiveness of the proposed method.