Full- and Reduced-Order Interval Observers for Linear Systems in Continuous and Discrete Time

This paper proposes a methodology for designing full-order and reduced-order interval observers for Linear Time-Invariant (LTI) systems, in both continuous and discrete-time settings, in the presence of uncertainties, disturbances, and measurement noise. The class of systems considered requires that the number of independent measured outputs be greater than or equal to the number of unmeasured states. The proposed approach enables the constructive assignment of the state matrix of the estimation error dynamics over the admissible Metzler–Hurwitz class compatible with the observer structure through an appropriate selection of the observer gains, ensuring both stability and cooperativity conditions without requiring the solution of Linear Matrix Inequalities. This flexibility facilitates the design of full and reduced-order interval observers for both continuous and discrete-time cases, generating upper and lower estimates that enclose the true state trajectory. Numerical examples are presented to illustrate the effectiveness of the proposed interval observer design methodology.