Robust ℌ∞ performance of periodic systems with memory: New formulations, analysis and design results

This paper is devoted to H_∞ analysis and synthesis conditions of state-feedback periodic memory controllers, in the framework of periodic uncertain discrete-time systems. The proposed conditions are such that the user is allowed to freely add degrees-of-freedom to the control law which effectively reduces the conservatism of the synthesis condition and decreases the guaranteed H_∞ induced norm of the obtained uncertain closed-loop systems. Numerical examples show that for a particular structure of controllers the efficiency of the design theorem can be significantly enhanced by relaxing the structure of slack-variables.