Extended high gain observer design

In this paper, an Extended High Gain Observer (EHGO) design for some classes of nonlinear systems with global Lipschitz nonlinearities, is proposed. The design is first proposed for a class of systems where the nonlinearities are triangular with respect to the state. Then, it is extended to another class of systems involving some unknown parameters that need to be estimated together with the state. Finally, the design is extended to a class of systems where the nonlinearities does not assume the usual triangular structure. Indeed, a more general triangular structure of the system is defined with respect to the state components which are reordered according to appropriate defined characteristic indices. The gain of the proposed EHGO is provided by a Lyapunov Ordinary Differential Equation (ODE). The observer convergence is guaranteed under an appropriate set of conditions given in terms of appropriate excitation. Simulation results are given for illustration purposes.