Symmetry-based observers for ODE systems

An observer design framework is introduced for ordinary differential equation (ODE) systems based on various types of existing or even novel one-parameter symmetries (exact, asymptotic and variational) ending up with different types of semi-global and global observers, by considering bounded or unbounded system solutions and requiring asymptotic- or prescribed-time error convergence. We compare some of these symmetry-based observers with existing observers, recovering for instance the same performances as high-gain semiglobal observers and the finite-time convergence capabilities of sliding mode observers.