Finite-time and fixed-time observer design: Implicit Lyapunov function approach

This work deals with the problem of finite-time and fixed-time observation of linear multiple input multiple output (MIMO) control systems. The proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed (defined a priori) time. Algorithms for the observers parameters tuning are also provided and a robustness analysis against input disturbances and measurement noises is carried out. The theoretical results are illustrated by numerical examples that consider both noisy and noise-free measurements and a comparison with a high-gain observer is included.