Control of Nonlinear and LPV Systems: Interval Observer-Based Framework

The problem of output stabilization of a class of nonlinear systems subject to parametric and signal uncertainties is studied. First, an interval observer is designed estimating the set of admissible values for the state. Next, it is proposed to design a control algorithm for the interval observer providing convergence of interval variables to zero, that implies a similar convergence of the state for the original nonlinear system. An application of the proposed technique shows that a robust stabilization can be performed for linear time-varying and linear-parameter-varying (LPV) systems without assumption that the vector of scheduling parameters is available for measurements. Efficiency of the proposed approach is demonstrated through two examples.

I. Introduction

The nonlinear system stabilization has been an area of active research during the last two decades [2], [9], [11]. Most of the proposed approaches appeal to particular structural characteristics of a given class of nonlinear systems. Frequently a partial similarity to linear systems is used to take advantage of the well established solutions for observer or control design. For example, the class of Lipschitz nonlinear systems forms a subclass of nonlinear ones, which can be estimated and controlled applying linear control approaches [13], [17]. This class of nonlinear systems is considered in the technical note under the assumption that the model is subject to uncertain time-varying parameters. The proposed methodology ensures stabilization for all parameter values belonging to a given interval.