In this paper, the problem of designing an observer for quadratically inner bounded (QIB) and one-sided Lipschitz (OSL) nonlinear systems considering perturbations in the output and unknown inputs is addressed. The observer synthesis procedures are formulated as convex optimisation problems. Sufficient conditions for observer gain synthesis are shown to be equivalent to solve finite sets of Linear Matrix Inequalities (LMIs) and Linear Matrix Equalities (LMEs). Three illustrative examples based on an isothermal CSTR reactor, a water tank-open channel system and FitzHugh–Nagumo system are used to illustrate how the proposed approaches are used to design the QIB-UIO scheme. The obtained simulation results are presented to assess the performance of the proposed method.

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