Distributed control of parameter-varying spatially interconnected systems using parameter-dependent Lyapunov functions

This paper considers the design of distributed controllers for spatially interconnected systems with varying parameters. Designed controllers inherit the spatial structure of the plant. To reduce the conservatism incurred by the use of constant Lyapunov functions, new linear parameter-varying synthesis conditions using parameter-dependent Lyapunov functions are proposed for multi-dimensional systems by extending previous results on lumped systems. The application of the full block S-Procedure leads to convex synthesis conditions. A bounded L₂ gain of the closed-loop system and its integral quadratic performance is guaranteed. The extended method is applied to a smart structure in simulation for performance illustration.