Reduced-order set-valued observer design for high order uncertain linear system with disturbance

For a class of high order uncertain linear system affected by parameter variations and disturbance, a reduced order observer is considered. A set-valued observer is designed for the main part of reduced-order observer, which estimates a convex cone containing the real states and fault states. The theoretical foundation of design of set-valued observer is uniformly boundness theory. By constructing a set-induced Lyapunov function, it can be proven that the estimation error converges to a compact set. Introducing the feedback control, the simulation figure shows that the estimation error converges to zero.