Observer-driven Switching Stabilization Of Switched Linear Systems

A switched system is a hybrid system which consists of a fnite number of linear sub-systems and a switching law governing the activeness of those subsystems. For switchedsystems, stabilization is not only an essential requirement, but also a hot research feldlasting for decades. A well-known characteristic of switched systems is that they includesboth continuous and discrete dynamics, which makes the system dynamics extremelycomplicated, and the stabilization design very tough. Especially for the stabilization de-sign in autonomous switched systems, for which the problem is to fnd, if possible, anappropriate switching law that makes the system asymptotically stable.For autonomous switched linear systems, when the system is consistently stabilizable,it has been established that a periodic switching signal could be found to solve thestabilization problem. Otherwise, state-driven switching mechanisms have to be soughtfor addressing the problem. Consider the fact that the state is usually unknown andcannot be measured directly in practice, an observer should be introduced. However, thedesign of the observer and the design of the stabilizing state-driven switching law are ingeneral coupled with each other as a common switching law is sought for both the originalsystem and the observer. This makes the observer-driven switching stabilization problemvery challenging.In this dissertation, we focus on the observer-driven switching stabilization problem.For this, we frst introduce some basic knowledge about the switched systems. On thisbasis, the main contents of this dissertation are summarized in the following:1. For switched autonomous linear systems whose subsystems are completely ob-servable, we frst introduce an improved less-overshooting observer design method, andthen consider the observer-driven switching stabilizing problem. A constructive path-wiseobserver-driven switching stabilization mechanism is proposed, by means of which, notonly the augmented system is stable, but also the design of the switching law and thedesign of the observer can be separated into two steps, thus a weak version of separationprinciple is established. Generally, to achieve stability with the observer-driven switchingstabilization scheme, we should implement the following steps. First, fnd a set of well- defned switching paths, whose corresponding contractive cones are a fnite partition ofthe state space. Second, place an observer based on the switching paths' minimal dwelltime. Finally, a path-wise observer-driven switching law is introduced.2. Relaxing the observability assumption to the observability of the switched linearsystem. For this, we frst study the observer design problem for observable switchedlinear systems, and proposed some observer design methods. Then by modifying theunobservable switching path to be observable, based on the path-wise observer-drivenswitching mechanism introduced before, an observer-driven switching law is given, whichmakes the augmented system stable. It is remarkable that the weak version of separationprinciple is also preserved.3. Consider the fact that perturbations can enter into any system, the robustnessis analyzed for system under structural, unstructural and switching perturbations. Tocapture the sensitivity of perturbed switching signals, the relative distance between thenominal and perturbed switching signals is introduced.4. As an illustrative example, the output-feedback stabilization problem for semi-active suspension vehicle is explored. Based on its switched linear system model, bymeans of the observer-driven switching stabilization mechanism, the problem is solved,and its robustness is proved.Finally, the conclusions and the prospects of future research are given at the end ofthis dissertation.