1 Department of Electronic Systems, The Technical Faculty of IT and Design, Aalborg University, VBN2 The Faculty of Engineering and Science (TECH), Aalborg University, VBN3 Aalborg University Space Center, The Technical Faculty of IT and Design, Aalborg University, VBN4 Automation & Control, The Technical Faculty of IT and Design, Aalborg University, VBN5 Aalborg U Robotics, The Faculty of Humanities, Aalborg University, VBN6 University of Guilan
This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix inequalities are brought forward, which determines the asymptotic stability of the Filippov solutions of a given uncertain piecewise linear system. Afterwards, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H∞ per- formance are formulated. Finally, a V-K iteration algorithm is proposed to surmount the aforementioned matrix inequality conditions.
Proceedings of the Ieee Conference on Control Applications, 2012, p. 1142-1147
Main Research Area:
I E E E International Conference on Control Applications. Proceedings
2012 IEEE Multi-conference on Systems and Control, 2012