Interval estimation for a class of discrete-time nonlinear systems with bounded Jacobian matrices via zonotopic analysis

This paper proposes a novel interval estimation method for a class of discrete-time nonlinear systems by integrating robust observer design with zonotope analysis. The system is reformulated into a linear part and a nonlinear remainder with a sign-constant Jacobian matrix. An (Formula presented.) -based unknown-input observer is designed to achieve simultaneous state and fault estimation. Building on this, zonotope analysis is employed to propagate the bounded uncertainties arising from the nonlinear remainder and measurement noise, thereby generating guaranteed interval estimates. The effectiveness and advantages of the proposed method are demonstrated through numerical simulations on a quadruple-tank system under fault scenarios.