Designing adaptive impulsive observer for a class of chaotic systems via linear matrix inequalities

This paper proposes a new class of observers, called adaptive impulsive observers (AIO). On the contrary to conventional observers which require output of the system continuously, AIO is capable to estimate the states of a nonlinear system by using the output of the system just at discrete instant times (impulses). Also, AIO would be able to estimate both states and unknown parameters of the uncertain system. Through Theorem 1 the asymptotic stability of the estimation error system is investigated and an upper bound on the maximum possible impulses interval is given. Also, the AIO design routine is simplified by modifying conditions of Theorem 1 to a set of LMIs in Theorem 2. AIO is applicable to many nonlinear systems, but because of its advantages it is used through a chaotic systems synchronization scheme. Presented simulation results show the effectiveness of the proposed observer even when the coupling signal is scalar.