Observer design for switching signal and states for a class of nonlinear impulsive switching systems

This paper presents a novel framework for designing an estimator capable of simultaneously estimating switching signals and state variables in nonlinear impulsive switched systems subject to unknown inputs. External disturbances and unknown inputs induce complex behaviors and impulsive effects in the observer, making accurate estimation highly challenging. A key innovation of the proposed structure lies in employing both a switching signal estimator and a nonlinear state estimator, which allows the nonlinear term to vary according to the active mode, thereby providing a more realistic representation of the system dynamics. Additionally, the matrix BBB, which represents the input coefficient, is variable and changes based on the system's dynamics. The existence and stability conditions of the proposed observer are derived through the Riccati equation and by solving multiple Linear Matrix Inequalities (LMIs). Furthermore, the stability of the estimation error is analyzed using the multiple Lyapunov function method. The effectiveness of the proposed approach is demonstrated through two application-oriented simulations. The first simulation involves a two-degree-of-freedom (2-DOF) robotic manipulator under different external forces, where the nonlinear term changes over time. The second simulation considers an electrical circuit in which the output dynamics vary due to nonlinear terms. Simulation results confirm that the proposed estimator can accurately reconstruct both the switching signals and state variables while effectively mitigating the impact of unknown inputs.