1 Aalborg University Space Center, The Faculty of Engineering and Science, Aalborg University, VBN2 Automation & Control, The Faculty of Engineering and Science, Aalborg University, VBN3 Department of Electronic Systems, The Faculty of Engineering and Science, Aalborg University, VBN4 Aalborg U Robotics, The Faculty of Humanities, Aalborg University, VBN5 The Faculty of Engineering and Science, Aalborg University, VBN6 Department of Electrical Engineering, Faculty of Engineering, University of Guilan, Rasht, Iran
A methodology to design guaranteed cost H∞ controllers for a class of switched systems with polynomial vector fields is proposed. To this end, we use sum of squares programming techniques. In addition, instead of the customary Carathéodory solutions, the analysis is performed in the framework of Filippov solutions which subsumes solutions with infinite switching in finite time and sliding modes. Firstly, conditions assuring asymptotic stability of Filippov solutions pertained to a switched system defined on semi-algebraic sets are formulated. Accordingly, we derive a set of sum of squares feasibility tests leading to a stabilizing switching controller. Finally, we propose a scheme to synthesize stabilizing switching controllers with a guaranteed cost H∞ disturbance attenuation performance. The applicability of the proposed methods is elucidated thorough simulation analysis.
Nonlinear Analysis: Hybrid Systems, 2014, Vol 11, p. 37-56