Quadratic Stabilizability of Switched Affine Descriptor Systems

This paper deals with a generalization of our recent results according to which impulse free switched affine descriptor systems can be quadratically stable via state-dependent switching law. The systems considered in our previous work are those which encompass finitely many modes modelized by linear nonhomogeneous differential systems (not necessarily stable) with the same algebraic constraints and such that the linear and affine parts are both commuted with different switching laws. Under some regularity and impulse-freeness assumptions, we prove that if there exist moreover some Hurwitz convex combination of subsystems matrices flows and if some convex combination of affine vectors is zero, then we can arrange a state-dependent switching law for which the entire switched affine DAEs system is quadratically stable at the origin. But when no zero convex combination of affine vectors exists, we have established that the switched affine descriptor system can be stabilized quadratically around an equilibrium point lying in a convergence set defined by the convex combination of the matrices flows and the affine vectors of each mode. The established results have wide variety of applications in engineering such as electric networks stabilization and robotics to named only those there.