Dissipative Proportional Integral Observer for a Class of Uncertain Nonlinear Systems

This paper proposes a dissipative proportional integral state observer for a class of uncertain nonlinear systems with sector-bounded nonlinearity. The L ₂ gain between disturbances and weighted estimation errors is adopted as the supply rate in the dissipativity framework, which guarantees the boundedness of state estimation errors. This estimator also includes an integral feedback loop on the output estimation error to improve steady-state estimation performance. In order to determine the optimal observer gains, the L ₂ gain minimization problem is formulated into a convex optimization problem subject to a linear matrix inequality. In addition, the concept of the exponential dissipativity is introduced to address the strict dissipativity in the observer structure.