Necessary and sufficient conditions for regional stabilisability of second-order switched linear systems with a finite number of subsystems

In this paper, the switching stabilisation problem of second-order switched linear systems is studied. By extending the best case switching signal (BCSS) criteria for second-order switched linear systems with two subsystems to the general case with any finite number of subsystems, necessary and sufficient conditions for regional stabilisability of second-order switched linear systems with any finite number of subsystems are proposed in this paper. The main idea of this paper is to divide all the subsystems in a region into two groups based on their trajectory directions in that region. By comparing pairwise, the most “stable” subsystem for each group in a region can be determined and the BCSS analysis among all the subsystems in that region is reduced to the BCSS analysis between the two most “stable” subsystems in that region.