A new procedure for modeling nonlinear systems via norm-bounded linear differential inclusions

There are several advantages of using linear differential inclusions (LDIs) to describe nonlinear systems and other types of complex systems (such as, systems with time-varying uncertainties and/or saturation). From the control point of view, for example, it may be easier to design a controller for a nonlinear system by using a linear description of it in the form of an LDI (instead of using the nonlinear equations for the same purpose). With this premise, we focus on modeling of a class of nonlinear systems via a norm-bounded LDI (NLDI) model. One of the main contributions of the proposed modeling approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying (LPV) model, which is then mapped into a polytopic LDI (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one of the main contributions of this paper. A numerical example is presented at the end of this paper to demonstrate the effectiveness of this approach.