The theory of switching systems has seen many advances in the past decade. Its beginnings were founded primarily due to the physical limitations in devices to implement control such as relays, but today there exists a strong interest in the development of switching systems where switching is introduced as a means of increasing performance. With the newer set of problems that arise from this viewpoint comes the need for many new tools for analysis and design. Analysis tools which include, for instance, the celebrated work on multiple Lyapunov functions are extensive. Tools for the design of switched systems also exist, but, in many cases, the method of designing stabilizing switching laws is often a separate process from the method which is used to determine the set of vector fields between which switching takes place. For instance, one typical method of designing switching controllers for linear, time-invariant (LTI) systems is to first design a set of stabilizing LTI controllers using standard LTI methods, and then design a switching law to increase performance. While such design algorithms can lead to increases in performance, they often impose restrictions that do not allow the designer to take full advantage of the switching architecture being considered.
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