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The vertical stabilizer is the key aerodynamic surface that provides anaircraft with its directional stability characteristic while ailerons andrudder are the primary control surfaces that give pilots control authority ofthe yawing and banking maneuvers. Losing the vertical stabilizer will,therefore, result in the consequential loss of lateral/directional stabilityand control, which is likely to cause a fatal crash. In this paper, weconstruct a scenario of a damaged aircraft model which has no physical ruddercontrol surface, and then a strategy based on differential thrust is proposedto be utilized as a control input to act as a "virtual" rudder to help maintainstability and control of the damaged aircraft. The $H_{\infty}$ loop-shapingapproach based robust control system design is implemented to achieve a stableand robust flight envelope, which is aimed to provide a safe landing.Investigation results demonstrate successful application of such robustdifferential thrust methodology as the damaged aircraft can achieve stabilitywithin feasible control limits. Finally, the robustness analysis resultsconclude that the stability and performance of the damaged aircraft in thepresence of uncertainty remain within desirable limits, and demonstrate notonly a robust, but a safe flight mission through the proposed $H_{\infty}$loop-shaping robust differential thrust control methodology.

Robust $H_{\infty}$ Loop-Shaping Differential Thrust Control Methodology  for Lateral/Directional Stability of an Aircraft with a Damaged Vertical  Stabilizer