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The controller is derived from an inner-outer loop control structure, namely by considering the position system coupled through an interconnection term with the attitude system. For the design of the position controller, the considered dynamics are worked on the body frame, which is uncommon in the literature, and its synthesis derives from theories such as Pontryagin\u2019s maximum principle, Lyapunov theory, and Linear Quadratic Regulator (LQR), which ensure Input-to-state stability, steady-state optimality, and global exponential stability. The attitude system is based on an error quaternion parameterization via a nonlinear coordinate transformation matrix followed by a state input feedback, rendering the system linear and time-invariant. Under a correct transformation, LQR theory ensures almost exponential stability and steady-state optimality for the overall interconnected closed-loop systems. Experimental and simulation results illustrate the performance of the tracking system onboard a quadrotor.<\/jats:p>","DOI":"10.1007\/s10846-023-02016-9","type":"journal-article","created":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T08:02:45Z","timestamp":1705046565000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Position and Attitude Tracking Controllers Using Lyapunov Transformations for Quadrotors"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2752-6398","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Madeiras","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7966-4648","authenticated-orcid":false,"given":"Carlos","family":"Cardeira","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5799-390X","authenticated-orcid":false,"given":"Paulo","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,12]]},"reference":[{"key":"2016_CR1","doi-asserted-by":"crossref","unstructured":"Idrissi, M., Salami, M.R., Annaz, F.: A review of quadrotor unmanned aerial vehicles: applications, architectural design and control algorithms. 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