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

Abstract

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