Gain Scheduled Control of Bounded Multilinear Discrete Time Systems with Uncertanties: An Iterative LMI Approach

In this paper a new approach for gain scheduled control design that can handle various multivariable controller stuctures is presented. Therefore, the class of multilinear discrete time systems is considered, which often occur in heating, ventilation and airconditioning (HVAC) applications. It is shown that the considered class of multilinear systems can be reformulated into the class of systems with convex polytopic uncertainty. Stability conditions in form of linear matrix inequalities (LMIs) are derived from a Lyapunov stability condition and an optimization problem to maximize the decay rate of the closed loop system is formulated. An existing algorithm formulation is applied to solve the optimization problem iteratively. The effectiveness of the proposed approach is demonstrated for a practical example and the flexibility of the approach is discussed.