Semi-Markov jump linear systems with bi-boundary sojourn time: Anti-modal-asynchrony control

This paper investigates the problem of control synthesis for a class of discrete-time semi-Markov jump linear systems, in which the sojourn time of each mode is bi-boundary (with upper and lower bounds). The system is subject to modal asynchrony, which means that the switchings of the mode-dependent controller to be designed lag behind the ones of the controlled plant, and the lag is mode-dependent. In contrast with the traditional mode-independent lag commonly assumed in the existing studies, not only is the modal lag more practical and general, but also it yields less conservatism of the controller design. By virtue of the semi-Markov kernel approach, the conditions on the existence of the anticipated stabilizing controllers capable of overcoming the modal asynchrony are derived. Illustrative examples including a class of vertical take-off and landing (VTOL) helicopter models are presented to demonstrate the necessity and the validity of the designed anti-modal-asynchrony controllers.