Unified Generalized H ₂ Nonlinear Parameter Varying Observer: Application to Automotive Suspensions

Abstract

This paper extends the unified observer design problem to the class of Nonlinear Parameter Varying (NLPV) systems with parameter dependence in both the dynamics and the control input matrices. First, parameterization of the observer matrices, herein generalized for the NLPV case, allows us to decouple the input disturbance from the estimation error. Then, the vanishing disturbance caused by the nonlinearity is bounded by the Lipschitz property and the effect of measurement noise on the error is minimized using the generalized H2 condition. Both objectives are combined into a single framework thanks to the S-procedure. Furthermore, the asymptotic stability of the error is tackled using a parameter-dependent Lyapunov function, then a grid-based Linear Matrix Inequalities (LMIs) solution is provided, which reduces conservatism. The efficiency of this observer is illustrated and compared with an LPV observer through the damper force estimation problem, a crucial topic in semi-active suspensions.