Gain scheduling has been applied to the practical engineering problems such as flight control, process control, etc. which require high performances. However, in the absence of a theoretical analysis, gain scheduling couldn't gaurantee the overall stability, performance, and robustness. In recent papers, [13][23], the analytical theories of gain scheduling are studied, but they didn't give any practical design methodology.
In this paper, a gain scheduling design algorithm is suggested in order to control a class of parameterized nonlinear systems with parametric uncertainties at set-points. Since each set-point corresponds to a scheduling parameter respectively, for a fixed scheduling parameter, we can design a $H_∞$ controller as a local robust controller, and determine the region with robust stability and performance by μ-method.
Then, the original nonlinear system is controlled by a finite set of local controllers which cover the whole operating points.
In simulations, the algorithm is applied to a pitch-axis autopilot design problem, and the robust stability and performance of a design local controller is gauranteed in its region.
