LMI-based nonlinear observer design for a class of nonlinear systems modeled with differential algebraic equations

This work presents a novel methodology to design nonlinear observers for a class of systems modeled as differential algebraic equations.The proposal is based on writing both the system and the observer as nonlinear descriptor redundancy representations subject to algebraic restrictions; then the nonlinear observation error system is written in an explicit incremental form via suitable factorization techniques.A redundant Lyapunov function is then employed to guarantee asymptotic stability of the estimation error; linearity of the Lyapunov function and its time derivative with respect to the observer gains and Lyapunov function terms, allows gridding or convex treatment of expressions via linear matrix inequalities.Physical examples are presented to illustrate the proposal effectiveness against former methodologies.