Control Synthesis of Singular PDT Switched Systems With State Constraints and Application to HyTAQs

This paper investigates the problem of control synthesis for a class of continuous-time singular switched systems, based on which a modeling and control framework is developed for Hybrid Terrestrial and Aerial Quadrotors (HyTAQs). To accurately describe the frequent switching phenomenon for HyTAQs during the landing process, persistent dwell time (PDT) switching signals are taken into consideration. Besides, mode-dependent state constraints are introduced to singular switched systems, which are more practical and general than the ones considered in earlier studies. Numerically testable stability criteria are obtained, and thereby the conditions on the existence of controllers capable of satisfying the mode-dependent state constraints are derived. Finally, two illustrative examples including HyTAQs are presented to demonstrate the necessity and validity of the designed controllers. Note to Practitioners—This paper is motivated by the modeling and stabilization of Hybrid Terrestrial and Aerial Quadrotors (HyTAQs), a class of vehicles with both terrestrial and aerial mobility, which have received extensive attention due to the low energy requirement and high maneuverability at the same takeoff weight. Note that the dynamic differences between aerial and terrestrial modes, exacerbate the challenges for performance analysis and controller design, let alone the differences in state dimensions. Therefore, the paper proposes a unified framework for modeling HyTAQs based on singular switched systems, and the mode-dependent state constraints are considered to reduce conservatism. In addition, the frequent switching phenomenon during the landing process has never been considered in the field. To this end, the PDT switching signals are introduced to describe the bounce and shake behaviors during the mode switching process. Numerically testable stability criteria are obtained, based on which the stabilization conditions for such systems are provided. Finally, a numerical example and an application for HyTAQs are presented to demonstrate the validity and applicability of the theoretical results.