Bumpless Transfer Control for Switched Systems: A Dual Design of Controller and Switching Signal

This article investigates the bumpless transfer (BT) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem for a class of switched linear systems. The key point is that a novel BT control framework exploiting controllers collaborated with switching signal (SS) design is proposed. This is based on the consideration that for most existing BT control strategies, the design of SS is only used to guarantee the stability of switched systems instead of the BT performance, while the BT performance is achieved by adding additional limitations to the original controllers, which makes it impossible to achieve both stability and BT performance simultaneously. A continuous switching controller with time-varying gain matrices is developed, which achieves continuous transition on the switching instants. A generalized time and state-dependent SS is designed, in which the dwell time provides enough regulation time to pursue a desired BT performance, while, the state-dependent switching relaxes the requirement on each system by allowing each subsystem to be unstable, which helps to realize a satisfactory steady-state performance. Besides, a sufficient condition verifying the solvability for the BT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem by the designed controller and SS is constructed. Finally, to demonstrate the availability of the proposed BT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control strategy, two examples are provided.