In modern control design problems, both frequency- and time-domain requirements are usually considered such that the resulting control law satisfies the specifications. Novel non-smooth optimisation techniques can be used to achieve multiple frequency-domain specifications over a family of linear models. Examples of applications include robust control design where multiple critical models for different values of the uncertain parameters are considered. This is illustrated in this thesis manuscript for a specific observer-based controller structure. However, enforcing time-domain constraints on a given output or state is more challenging since translating them into frequency-domain requirements may be unclear and inaccurate in real-world applications. This motivates the study of a new approach to the aforementioned H∞ control design techniques. When time-domain constraints are satisfied, the nominal control law reduces to the structured controller synthesized against frequency-domain constraints. Upon violation of the time-domain constraint, an additional tool named OIST is used to appropriately saturate the controller output so as to restrict the reachable set of the constrained system output. Satisfying results as well as stability guarantees are obtained for minimum phase systems. Further developments proposed in this thesis allow the consideration of uncertain systems with incomplete state measurements. This is the novel OISTeR approach. The method requires the knowledge of certified bounds on the considered system state. Such information is accessible through using interval observers. The theory of interval observers is well-established. In the case of linear systems, the most common approach is to consider an intermediate cooperative system on which the interval observer can be built. For a given linear system, a cooperative representation can be obtained in new coordinates using a time-invariant state-coordinate transformation. The transformation determination methods are easy to use but lack versatility especially when performance guarantees on the interval tightness are required. This motivates the novel SCorpIO design method proposed in this work which relies on the reformulation of the original mathematical problem into a structured control-design problem. In this thesis, the considered application is the atmospheric control of a flexible launch vehicle in the presence of wind gusts. It is critical that the angle of attack of the vehicle should remain bounded to limit the aerodynamic load on the structure. Using the techniques developed in this thesis, solutions are proposed for a simplified launch vehicle model. Perspectives are drawn for future developments on more complex problems.