On conditions for regularity of solutions for a piecewise linear system

Two types of limit cycles of a resonant converter modelled by a three-dimensional system

“…We have reported corresponding symmetry in the two-dimensional case earlier (Melin and Hultgren [18,17]). As a consequence, possible limit cycles and possible other types of non-wandering sets of (5) must be preserved or reflected onto other similar co-existing nonwandering sets under the same geometric transformation.…”

“…The first case consists of limit cycles entirely inside the switching surfaces defined by the cylinder, introduced in section 4, and the second case consist of a special type of limit cycles that occur both inside and outside the cylinder, introduced in section 5. Both of these cases are studied through projections onto two-dimensional systems close to the two-dimensional approximation analyzed previously by Melin and Hultgren [18]. We summarize the results in section 6 and indicate some ideas for future research.…”

“…If |z| > U 0 , thenż = 0, and the system reduces by definition into the two-dimensional system studied in Melin and Hultgren [18]. The application itself makes these cases of limited interest, too.…”

“…In this analysis a resonant power converter is modelled as a switched system and it is controlled by a switched controller. In Hultgren and Lenells [11] and Melin and Hultgren [18] a detailed description of the electrical converter is given. In the latter reference also an analysis of a second order switched model of the system is given.…”

“…The last plane contains the main axis of the cylinder and is therefore perpendicular to the other planes, see Figure 2. Two-dimensional approximations describing resonant converters by switched systems have been studied previously by Melin and Hultgren [18]. Generally, extensions of the classical Poincaré-Bendixson theory (e. g. Hirsch and Smale [8]) and extensions of currently existing tools for estimating the number of limit cycles from above (e. g. Ye et.…”