Abstract
In this paper, an extremely simple control approach is proposed for the multichain systems. This method is based on a switching of two sets of control laws. Each law is given by a product of the generator and a time-invariant linear function of the state. The switching is based on the sign change of the generator. Global exponential convergence of all states is guaranteed. More importantly, the convergence rate is given explicitly. A remarkable feature of the proposed approach is that in each phase of the switching control, the ratio of state convergency is an exponential function of the displacement of the state driven by the generator. For the design of each control law, two methods are proposed.
