New results on regional observer-based stabilization for locally Lipchitz nonlinear systems

This paper describes the design of a regional observer-based controller for the locally Lipchitz nonlinear systems, which can be employed successfully to attain both monitoring and control of a wide range of systems. An observer-based control approach has been employed to attain advantages of the traditional state feedback along with the state estimation through an observer. A lot of work has been accomplished for the globally Lipchitz nonlinear systems. However, a less conservative continuity, called the generalized ellipsoidal Lipchitz condition, has been applied in this paper to consider the locally Lipchitz systems. This condition is then incorporated to attain convex routines for computing the local controller and observer gains. The focus of the present study is to investigate conditions for simultaneous design of observer and controller under locally Lipchitz nonlinearities for systems with norm-bounded disturbances that not only guarantees the stabilization and true state estimation but also robustness against external perturbations. Furthermore, the decoupling of the observer and controller design conditions has been worked out for obtainment of a simple design method. Since the resultant control approach applies to a general class of systems, it can be straightforwardly employed to the globally Lipschitz nonlinear systems as a specific case. The approach is tested via a chaotic system and simulation results are provided to validate the effectiveness of resultant control schemes for the locally Lipschitz systems.