A. Dehghani, M. Rotkowitz, B.D.O. Anderson and S.H. Cha
Simplified Rapid Switching Gain Scheduling for a class of LPV Systems
IEEE Transactions on Automatic Control, vol. 57, no. 10, pp. 2633-2639, October 2012.


A limitation of the original gain-scheduling approaches is that the closed-loop stability can only be assured when the underlying parameters vary sufficiently slowly. A remedy exists but requires for its implementation the possible solution of asymptotic Riccati equations (ARE) for an infinite number of different parameter values, and the on-line solution of a Riccati differential equation (RDE) with time-varying coefficient matrices. Our method avoids solving the RDE online and instead uses an explicit transient formula that looks up the predetermined solutions of the associated AREs at a finite set of given system operating points. Furthermore, only a finite number of AREs are solved to determine a finite set of controller gains.