Partly gain scheduled controller based on parameter dependent Lyapunov matrix

It is well known that the gain scheduled controller is effective for parameter-varying systems. By using parameter dependent Lyapunov matrix, the performance of the gain scheduled controller is significant. However, the controller gain is calculated by using the inverse of the Lyapunov matrix in ordinary linear matrix inequality framework. When the parameter dependent Lyapunov matrix is applied, the real-time computational burden for the inverse of the parameter dependent Lyapunov matrix cannot be ignored. In this paper, we propose a partly gain scheduled controller synthesis that requires less computational burden for the inverse of parameter dependent matrix. We choose sub-state variables to apply gain scheduling and synthesize a gain scheduling controller for the subsystem. It allows using a lower order parameter dependent matrix in the online calculation. After applying the local gain scheduling controller, we synthesize full state static feedback gain to stabilize the total system by using a parameter dependent Lyapunov matrix. By using a parameter dependent Lyapunov matrix to synthesize the static gain, we expect to reduce some conservativeness.