High-gain observer for 3 × 3 linear heterodirectional hyperbolic systems

Abstract

The problem of High-Gain Observer Design is addressed for a class of 3 × 3 inhomogeneous linear hyperbolic systems with possibly distinct characteristic velocities and considering distributed measurement of part of the state. Applying an infinite-dimensional state transformation, the system is mapped into a new set of partial differential equations, satisfying an appropriate form for observer design. The observer includes output correction terms and also spatial derivatives of the output, and ensures arbitrarily fast state estimation. The result is illustrated with a simulated example.