Worst-case analysis and design of sampled-data control systems

Sampled-data systems with continuous-time inputs and outputs, where some state variables evolve in continuous time and others evolve in discrete time, are considered. Methods are presented for computing and optimizing the L₂-induced norm of such systems, considered as operators relating square integral signals. These worst-case analysis and design results are counterparts of the H_∞-norm analysis and synthesis for purely continuous- or discrete-time systems. The analysis shows that the L ₂-induced norm of a sampled-data system is smaller than γ if certain discrete-time descriptor systems have no eigenvalue of magnitude one, and if a certain discrete-time linear time-invariant plant depending on γ has H_∞ norm smaller than γ. The synthesis shows that the optimal attenuation problem for a four-block continuous-time plant with a digital controller can be solved with a γ-iteration on a certain discrete-time four-block plant which depends on γ