Decentralized Observer Design for a Class of Nonlinear Uncertain Large Scale Systems with Lumped Perturbations

Many valuable properties of the state feedback method can not be applied to some class of control systems while some of the system states cannot be measured directly. An attractive alternative approach is to make good use of a state observer. In this paper, a new decentralized sliding mode observer DSMO is proposed for a class of nonlinear uncertain large-scale systems LSS with lumped perturbations based on the sliding mode control SMC theory. Our main result presented here is that we introduce a new switching term to the traditional LSS observer design for a class of large-scale system to generate a new decentralized sliding mode observer. The generalized matrix inverse concept is adopted to avoid using the un-measurable state and the global reaching condition of the sliding mode for each error subsystem is guaranteed. The stability of each equivalent error subsystem is verified based on the strictly positive real concept. It also shows that the investigated uncertain large-scale systems still possesses the property of insensitivity to the lumped perturbations as does the traditional linear system. Moreover, the state transformation approach is no longer needed as there is no longer concern about the problems of finding a suitable transformation or indirect estimated states, since the proposed DSMO is not based on the transformed system model. Finally, a numerical example with a series of computer simulations is given to demonstrate the validity of the proposed decentralized sliding mode observer.