Convergence of full-order observers for the slow states of a singularly perturbed system (Part I: Theory)

Estimation of physical variables of nonlinear systems with two-time scales is a hard task to address. Whilst nonlinear systems exhibiting a singularly perturbed structure are common in engineering applications, current observer design results apply only to a specific class of plants and observers. We consider a broader class of plants and observers to generalise existing results on observer design for slow states of nonlinear singularly perturbed systems. Under reasonable assumptions, it is shown that the estimation error can be made semi-globally practically asymptotically stable in the singular perturbation parameter. This subsequently leads to appropriate conditions for the observer design for slow variables that guarantee satisfactory estimation error performance in the full system.