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In this chapter, the design of delay-dependent and delay-independent full-order unknown input observers is proposed for the class of linear time-invariant systems with state and input delays. The necessary and sufficient conditions for asymptotic stability, and existence conditions of the two observers, are provided. The efficiency of the proposed algorithms is illustrated using the quadruple-tank benchmark, in which the case of the nonminimum phase model is considered.

In this paper, an unknown input observer is proposed for linear systems with state and input delays. The robust observer designed is for a delay-dependant system. Necessary and sufficient conditions are provided for asymptotic stability and existence conditions. The efficiency of the proposed algorithm is validated using the quadruple–tank benchmark as a case study of the non-minimum phase systems.

In this work, we consider the design problem of a full-order and also reduced-order unknown input observers for a particular class of time-delay systems. Asymptotic stability and existence conditions for the designed observers are established. The quadruple-tank process is used as a benchmark to prove the efficiency of the proposed algorithms.

In this paper, a design of a full-order observer for linear time-invariant (LTI) multivariable systems with multiple time-delays and unknown inputs (UI) is proposed. The main idea is to reduce the problem of the unknown input observer (UIO) for systems with multiple time-delays to that of a standard one. To that purpose, the orthogonal collocation method is used to transform the infinite dimensional model of the delayed system described by a set of linear partial differential equations (PDEs) to a finite dimensional one described by a set of linear ordinary differential equations (ODEs). Even using an approximation method, the asymptotic stability of the UIO is well proven. The efficiency of the proposed algorithm is shown using the quadruple-tank benchmark. The two cases of minimum and non-minimum phase models are considered.

This work proposes a new design of a full-order observer able to achieve reconstruction of the state vector of LTI multivariable systems with multiple time-delays and unknown inputs (UI). The basic idea is to transform the problem of the unknown input observer (UIO) for LTI multivariable systems with multiple time delays to that of a standard one. The observer algorithm is achieved in three stages. First, the LTI multivariable system with multiple delays and UI is transformed into a distributed parameter system (DPS) described by linear partial differential equations (PDEs). Then, using the orthogonal collocation method, the DPS is reduced in a lumped system described by linear ordinary differential equations (ODE). Finally, the problem of the UIO design for the reduced system is solved. The efficiency of the proposed algorithm is finally illustrated using the non-minimum phase model of the 4-tank benchmark.