A switching dynamical system by means of piecewise linear systems in R^3 thatpresents multistability is presented. The flow of the system displays multiplescroll attractors due to the unstable hyperbolic focus-saddle equilibria withstability index of type I, i.e., a negative real eigenvalue and a pair ofcomplex conjugated eigenvalues with positive real part. This class of systemsis constructed by a discrete control mode changing the equilibrium pointregarding the location of their states. The scrolls are generated when thestable and unstable eigenspaces of each adjacent equilibrium point generate thestretching and folding mechanisms to generate chaos, i.e., the unstablemanifold in the first subsystem carry the trajectory towards the stablemanifold of the immediate adjacent subsystem.
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