High‐order sliding‐mode functional observers for multiple‐input multiple‐output (MIMO) linear time‐invariant systems with unknown inputs

For arbitrary multiple-input multiple-output linear time invariant systems with unknown inputs this article provides sufficient conditions to estimate functionals of the state variables. When input is uniformly bounded these are strictly weaker than classical for functional observers, well-known in literature, and generalize previous results using discontinuous differentiators. Furthermore, a general methodology proposed design that able functionals, when possible, exactly finite-time or fixed-time. Instead cascade Luenberger observers high-order sliding-mode differentiators, standard literature problem, bi-homogeneous observer reduced order article. Proofs convergence provided smooth Lyapunov functions an academic example illustrates behavior system not tractable available methods.