Constrained unidirectionally connected FASs: Part III. Applications

In this paper, applications of the sub-stabilisation technique proposed in Duan (Constrained unidirectionally connected FASs: Part II. Sub-stabilisation. International Journal of Systems Science, 2025a, https://doi.org/10.1080/00207721.2025.2467223) for the big type of unidirectionally connected fully actuated systems (UC-FASs) introduced in Duan (Constrained unidirectionally connected FASs: Part I. Models. International Journal of Systems Science, 2025b, https://doi.org/10.1080/00207721.2025.2466806) are considered. By using the proposed sub-stabilisation technique, a unified solution is provided to sub-stabilisation of a series of equivalent systems extended from the practical backgrounds of several types of maneuvered moving objects (MMOs), which include the well-known planar vertical taking-off and landing (PVTOL) system as a special case. A sub-stabilising controller is designed, which produces a closed-loop system composed of two time-invariant linear systems with arbitrarily prescribed eigen-polynomials. The corresponding region of exponential attraction (RoEA) is provided and intuitively presented. Assured by theory, as long as the system initial values lie within the characterised RoEA, the closed-loop response converges exponentially to zero within the set of feasibility. Simulation results for the PVTOL system demonstrate the effect of the proposed approach.