Stability test based on eigenvalue loci for bimodal piecewise linear systems

We consider convergence and stability analysis for a class of bimodal piecewise linear systems. We first discuss some properties of trajectories of bimodal piecewise linear systems and derive a necessary condition and a sufficient condition for the stability. The conditions are given in terms of the eigenvalue loci and the detectability of subsystems. In addition, we provide two necessary and sufficient conditions for the planar bimodal piecewise linear systems to be stable. These two conditions are given in terms of eigenvalue loci of subsystems and coefficients of characteristic polynomials, respectively. Furthermore, we discuss a stabilizing controller design based on the derived sufficient condition.