Robust gain-scheduled control of a vertical takeoff aircraft with actuator saturation via the LMI method

This paper presents a robust gain-scheduled approach for the control of a vertical/short takeoff and landing (V/STOL) aircraft. The nonlinear aircraft dynamics exhibit non-minimum phase characteristics arising from the parasitic coupling effect between the aircraft's lateral force and rolling moment. The undesired coupling effect also causes modelling uncertainty of the aircraft dynamics. The nonlinear aircraft dynamics are considered to be composed of a nominal linear parameter varying (LPV) system and a linear system with a norm bounded uncertainty matrix multiplied by the parasitic uncertain non-minimum phase coupling parameter. The nominal LPV system is considered to be affinely dependent on a measurable varying parameter. The ranges of the varying parameter and its variation as well as its parasitic induced uncertain matrix are addressed by introducing the parameter-dependent invariant ellipsoid interpretation for dealing with the issue of affinely quadratic stabilization. The relations among the magnitude of actuator saturation, the maximum achievable relative stability, and the sustainable coupling uncertainty are investigated for the considered robust gain-scheduled design.