Stabilizing Sequence Search for Time-Controlled Switched Nonlinear Systems with All Unstable Modes

One of the important problems in time-controlled switched dynamical systems is to find a stabilizing time sequence if there is any. The problem is challenging for switched systems with all unstable modes. Two fundamental approaches are introduced, which are classified as the fast switching method and the method of converting state-controlled signals. Five schemes are delineated and validated in the numerical study based on the two approaches. The effects of switching frequency and duty ratio on the dynamical system performance are analyzed, from which important implications have been drawn for use in practical system design. The proposed methods shall also provide intuition into understanding the mechanism of how to maintain a dynamical system’s stability when all of its modes are unstable.