LMIs in Control/Applications/F16 Longitudinal Stabilitzation

F-16 Longitudinal Stabilization using Hinf Output Feedback The linearized longitudinal dynamics of the F-16 aircraft are considered in this example. The nonlinear 6DOF model is linearized using straight-and-level flight conditions of: See chapter 3 of [] for further details. The System The state-space representation for the linearized longitudinal dynamics can be written as follows: where , , , and are the state variable, control input, disturbance, and regulated output vectors, respectively. In this case, is velocity (ft/s), is angle of attack (rad), is pitch (rad), is pitch rate (rad/s), is elevator deflection with respect to trimmed deflection (rad), is commanded elevator deflection with respect to trimmed deflection (rad), and is normal acceleration at the pilot location (ft/s^2). The Data For the linearization used, the above matrices are: The LMI: Optimal Output Feedback Control LMI The following are equivalent. 1) There exists a such that 2) There exists , , , , , , such that Conclusion: Using this problem formulation, an output controller can be found that attenuates normal acceleration and tracks reference elevator deflection command. Implementation Related LMIs References Stevens, Brian L., et al. Aircraft Control and Simulation. Third ed., Wiley, 2016.