Observer-based H∞ control using the incremental gain for one-sided Lipschitz nonlinear systems

In this paper, an H_∞ output feedback controller is presented for one-sided Lipschitz systems, which consists of a state feedback control together with a nonlinear observer. By proposing the L₂ incremental gain as an alternative H_∞ performance measure to the usual gain, we develop a design technique that guarantees an asymptotically stable closed-loop system in the absence of disturbance inputs and further minimizes the incremental gain from disturbances to the controlled output. This method is based on the Lyapunov function parametrization and is formulated in terms of linear matrix inequalities (LMIs). Our result is then validated via numerical example of a discontinuous plant exposed to disturbance inputs with numerous variations.