Finite-time and fixed-time observers design via implicit Lyapunov function

This paper deals with the problem of finite-time and fixed-time observation of linear multiple input multiple output (MIMO) control systems. The nonlinear dynamic observers, which guarantee convergence of the observer states to the original system state in a finite and a fixed (defined a priori) time, are studied. Algorithms for the observers parameters tuning are also developed. The theoretical results are illustrated by numerical examples.