Pole assignment of two-dimensional switched linear time- invariant systems with multiple equilibria

Abstract

This paper discusses the pole assignment issues of two-dimensional switched linear time-invariant (LTI) systems with multiple equilibria. For the case in which each subsystem has a unique equilibrium point, a necessary and sufficient condition of arbitrary pole assignments for such switched LTI systems with multiple equilibria is proposed. A numerical example shows that even when all the poles of all the closed-loop subsystems are assigned to only two locations on the left-half side of the complex plane, the overall switched LTI systems may not be stable under arbitrary switching. For switched systems in which all the subsystems have a common single equilibrium point or different multiple equilibria, several sufficient criteria of stabilizing pole assignments and corresponding algorithms are proposed. The results imply that to stabilize switched LTI systems via the pole assignment method, all or some of the poles of some or all the subsystems can be assigned to suitable locations on the right-half side of the complex plane. An illustrative example shows that our new results are very effective and practical.