Prescribed-Time Unknown Input Observers for Linear Time-Varying Systems With Applications to Aerospace Systems

This paper addresses the problem of the design of prescribed-time unknown input observer (UIO) for linear time-varying (LTV) systems. Employing a nonsingular time-varying transformation, the completely observable LTV system with unknown input is converted into the observable canonical form, regardless of whether it is lexicographically fixed or non-lexicographically fixed. Building upon the obtained observable canonical form, the prescribed-time UIO is devised by fully utilizing the characteristics of the parameter Lyapunov equation (PLE). Then, by choosing a suitable Lyapunov-like function, it will be demonstrated that the error of the observer approaches zero within a designated time. Two simulation examples of aerospace systems confirm the reliability of the designed prescribed-time UIO.