As the utilization of stratospheric airships becomes more prevalent, ensuring their safe operation becomes crucial. This paper explores the ability of an L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}_{1}$$\\end{document} adaptive controller to maintain fault tolerance in the actuators of a stratospheric airship. L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}_{1}$$\\end{document} adaptive control offers fast adaptation while separating adaptation and robustness. This makes the approach a suitable candidate for fault-tolerant control. The performance of the proposed design is compared to the Linear Quadratic Integral and Adaptive Sliding Mode Backstepping controllers. Simulation results show that the robustness of the airship model against faults is improved with the use of the L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}{}_{1}$$\\end{document} adaptive controller.