Stability margins in adaptive mixing control via a Lyapunov-based switching criterion

In all classes of linear adaptive control that involve switching or not there is no guarantee that after the switching stops or the adaptation is switched off the resulting closed loop linear time invariant system is stable let alone have a certain stability margin unless the persistence of excitation condition is satisfied. It will be of great practical importance if in the case of switching adaptive control we can converge to a controller that is stabilizing with certain stability margins. In this paper, a switching logic ensuring Lyapunov stability is proposed inside the framework of adaptive mixing control (AMC). The switching logic uses a Lyapunov based criterion to assess which controller should be put in the loop. The resulting scheme guarantees that the final switched-on controller satisfies a Lyapunov inequality implying a prescribed stability margin. A numerical example is used to show the effectiveness of the method.