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This paper proposes a tractable family of remainder-form mixed-monotonedecomposition functions that are useful for over-approximating the image set ofnonlinear mappings in reachability and estimation problems. In particular, ourapproach applies to a new class of nonsmooth nonlinear systems that we calleither-sided locally Lipschitz (ELLC) systems, which we show to be a supersetof locally Lipschitz continuous systems, thus expanding the set of systems thatare formally known to be mixed-monotone. In addition, we derive lower and upperbounds for the over-approximation error and show that the lower bound isachievable with our proposed approach. Moreover, we develop a set inversionalgorithm that along with the proposed decomposition functions, can be used forconstrained reachability analysis and interval observer design for continuousand discrete-time systems with bounded noise.

Tight Remainder-Form Decomposition Functions with Applications to Constrained Reachability and Interval Observer Design