An LMI approach to dissipativity-based control of nonlinear systems

Abstract

In this article, a new LMI method to control of discrete-time nonlinear systems based on the dissipativity theory is presented. In this approach, a nonlinear system is considered as a linear part in addition to a nonlinear term. In order to attain a quadratic bound for the nonlinear term, a sum of squares (SOS) optimization problem is solved. Dissipativity condition of the system is given using a discrete storage function and a quadratic supply rate. Consequently, a state feedback control law is obtained to ensure the system’s dissipativity. In addition, two other LMI-based optimization problems are introduced to get the maximum area domain of attraction of the nonlinear system that is a subset of the region of dissipativity. Finally, two practical nonlinear systems including a continuous stirred tank reactor (CSTR) and a quadruple-tank process are simulated to show the applicability and accuracy of the proposed dissipativity-based control approach for nonlinear systems.