On robust state estimation for linear systems with matched and unmatched uncertainties

This paper addresses the problem of robust observer design for linear dynamic systems with uncertain parametric state matrix. Two class systems with non-bounded parametric uncertainties are considered for estimation: dynamic systems with matched conditions and dynamic systems with unmatched conditions. In this context, a robust estimator with a second gain update output estimation error is developed to linear systems with matched uncertainties. The framework is generalised to linear systems with unmatched uncertainties. With lesser restrictive conditions, it is shown that the conceived estimator for a chosen nominal system is insensitive to non-bounded parameters variation and provides good performances. Analytical developments are detailed and adopted choices are justified. Upon satisfying some conditions, the convergence properties of the robust estimators are proved through Lyapunov method. Approaches validity are illustrated via detailed numerical examples with extensive simulation results.