M. Hajiahmadi, B. De Schutter, and H. Hellendoorn, "Robust H∞ control of a class of switched nonlinear systems with application to macroscopic urban traffic control," Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, California, pp. 1727-1732, Dec. 2014.
This paper presents stability analysis and robust H_∞ control for nonlinear switched systems bounded in sectors with arbitrary boundaries. By proposing new and more general multiple Lyapunov functions that incorporate nonlinearities in the system, we formulate the stability conditions under arbitrary switching in the form of linear matrix inequalities. Moreover, an optimization problem subject to bilinear matrix inequalities is established in order to determine the minimum L2-gain along with the optimal matrices for the Lyapunov functions and for the robust state feedback gains. Finally, the optimization problem is recast as a bi-level convex optimization problem using loop transformation and other linear matrix inequalities techniques. Furthermore, in order to illustrate the performance of the proposed switching control scheme, results for control of an urban network partitioned into sub-regions and modeled using a high-level hybrid model are presented.