Design of Second-Order Sliding-Mode Controller via Output Feedback

The work is centered on developing a constructive method of synthesizing an output-feedback second-order sliding-mode (SOSM) controller. By leveraging a coordinate transformation and revamping the technique of adding a power integrator, a state-feedback SOSM controller is first constructed under the full-state measurement. In order to tackle the challenge posed by the unmeasurable first derivative of the sliding variable, a discontinuous observer with appropriately selected scaling gains is put forward to overcome the measurable lack. Through the interactive cooperation of the state-feedback SOSM controller and the discontinuous observer, an output-feedback SOSM controller is successfully designed without reliance upon the separation principle. The finite-time convergence of the whole system is rigorously validated by dint of the Lyapunov function-based analysis. The efficiency of the theoretical results is ultimately corroborated through a simulation study.