Quadratic Stability of Switched a ne DAEs Via State-Dependent Switching Law

Abstract

In this paper, we deal with quadratic stabilization for a particular class of impulse-free switched differential affine algebraic systems (switched affine DAEs) which consisted of a finite set of affine subsystems with the same algebraic constraint, where both subsystem matrices and affine vectors in the vector fields are switched independently and no single subsystem has desired quadratic stability. We show that if a convex combination of subsystem matrices such that the result LTI algebraic system is assymptotically stable, and another convex combination of affine vectors is zero, then we can design a state-dependent switching law such that the entire switched affine DAEs system is quadratically stable at the origin. But when the convex combination of affine vectors is not zero, we discuss the quadratic stabilization to a convergence set defined by the convex combination of subsystem matrices and the convex combination of affine vectors.