Constrained switching stabilization of linear uncertain switched systems using piecewise linear Lyapunov functions

The problem of switching stabilizability of linear uncertain switched systems with unstable modes has recently attracted increased interest. For a given collection of unstable linear uncertain subsystems, the problem is to determine asymptotically stabilizing switching signals or to ascertain the absence of such laws. In this paper, we deal with the switching stabilizability problem for a class of autonomous continuous-time switched linear systems with time-varying parametric uncertainties in the presence of additional state constraints. With a special emphasis on two-dimensional systems we extend previous relevant results in the literature, and we propose a computational technique that generates piecewise linear Lyapunov functions of a convex or non-convex nature. The algorithm is graph-based and consists of determining controlled invariant polytopes induced by systematic conic decompositions of the state-space and corresponding state-dependent switching control actions. Further extension of this computational tool to higher dimensional systems is also discussed.