Aircraft controller design to enhance longitudinal maneuvers

In many cases, we can linearize the dynamical equations of a nonlinear system depending on a parameter, for each value of that parameter around any equilibrium point. As a result, the obtained matrices of the linear model also depend on that parameter and equilibrium point. Thus, corresponding to any value of that parameter, exists a linear controller that at that point and its neighborhoods can achieve satisfactory efficiency metrics; but outside of this neighborhood there isn´t any guarantee to fulfill the minimal performance requirements. In the gain-scheduling method, we linearize the system for several points within the spanning domain of the parameter and for any of these linear models will design controllers to switch into them depending on some criteria. In this paper, the problem of determining multiplicity of equilibrium pints in gain-scheduling method for an aircraft to have longitudinal movement is considered. Also we seek to find a criterion to tell us when each particular controller should be used which is carried out through stability margin observations and the v-Gap metric.