Projectional Observers of Nonlinear Systems with Full-State Constraints

The aim of this brief was to develop a class of state estimator modified with a projection function to reconstruct the non-measurable variables of a state-constraint system. The main characteristic of this observer was that the estimated states remain inside the compact set defined by the given variables constraints, independently of the output noise and internal modeling uncertainties. The application of the projection operator introduced a non-smooth form for the observer design. Hence, integral Lyapunov functions can be used to realize the stability study. The design of a Lyapunov-Krasovskii functional overcome the smoothness problem and justifies the ultimate boundedness of the estimation error. The upper bound for the estimation error is rationally related to the observer's lag and it is nonlinear associated with the power of output noises and modeling errors. Two numerical examples (the Chua's circuit and the ozonation of toxic compounds adsorbed in soil) illustrated the application of the suggested observer.