Observer-based stabilisation of linear systems with parameter uncertainties by using enhanced LMI conditions

Abstract

This paper deals with the problem of observer-based stabilisation for linear systems with structured norm-bounded parameter uncertainties. A new design methodology is established thanks to a judicious use of some mathematical artefacts such as the well-known Young inequality and various matrix decompositions. The proposed method allows one to compute simultaneously the observer and controller gains by solving a single bilinear matrix inequality (BMI), which becomes a linear matrix inequality (LMI) by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples and evaluations of the conservatism are provided to show the effectiveness of the proposed design methodology.