The classical LMI framework for robust multi-objective analysis is extended from time-invariant to time-varying systems. Results concern both input-output performances and bounds on times responses such as the damping ratio. State-feedback is considered using the Svariable approach which allows, at the difference of the Lyapunov Shaping Paradigm, to search for several Lyapunov certificates simultaneously, one for each performance requirement of the multi-objective problem. Results are illustrated by local stabilisation of a non-linear plant with several performance specifications.