Sensor delay-compensated prescribed-time observer for LTI systems

We present an observer for linear time-invariant (LTI) systems with measurement delay. Our design ensures that the error converges to zero within a prescribed terminal time. To achieve this, we employ time-varying output gains approach infinity at time, which can be arbitrarily short but no shorter than sensor delay model as transport partial differential equation (PDE) and build upon cascade ODE–PDE setting while accounting infinite dimensionality of sensor. construct our gains, needs conducted in particular system representation. For this reason, sequence state transformations (and their inverses) mapping original into (1) form, (2) delay-compensated form via backstepping, (3) diagonal is amenable selection prescribed-time stabilization. construction uses (a) generalized Laguerre polynomials, (b) elementary symmetric (c) polynomial-based Vandermonde matrices. A simulation illustrates results.