A unified framework for switched systems with smooth transfer of both control input and state

This paper investigates the smooth transfer (ST) control for a class of discrete-time switched linear systems. A unified ST (UST) framework that simultaneously suppresses the bump of both control input and state, occurring not only at switching instants but also within subsystems, is proposed with stability and H_∞ performance guarantee. The design consists of a set of transition-dependent ST (TST) and mode-dependent ST (MST) controllers. Specifically, TST controllers suppress the bump at switching instants using a sequence of time-varying gains, which serve to bridge between MST controllers that are activated within subsystems. Compared with existing studies, which are typically over-designed, the TST and MST controller gains in UST are optimized in a unified framework, and are no longer pre-given or forced to be the same. Moreover, the more challenging and general case of asynchronously nondeterministic switching in UST is tackled for the first time, and the obtained results also include synchronous switching as a special case. Finally, a numerical example and an application to F-18 flight control are employed to demonstrate the potential of the theoretical findings.