Novel Nussbaum Design for Nonlinear Systems With Unknown Switching Control Directions

This brief investigates the stability of switched nonlinear systems with input saturation and multiple unknown switching control directions using a novel Nussbaum design. The conventional Nussbaum design cannot be applied here directly because the multiple Nussbaum-type functions may cancel each other. To address the challenges posed by the unknown control directions, a novel variants of the Nussbaum-type function tailored to mitigate this limitation is introduced herein. The proposed control approach accounts for the input saturation constraints, while the system stability is verified using the average dwell time method. The approach is numerically validated on a jerk circuit system, demonstrating the effectiveness of the proposed design.