In This Thesis, The Problem Of Controller Design For An Over-Actuated System Is Dealt In Two Stages; First To Design A Controller For A Set Of Virtual Control Inputs And Second To Obtain A Control Allocation Strategy To Distribute These Virtual Inputs Among The Actuators. The Controller Is Synthesized For The Virtual Inputs By Minimizing The Infinite Norm Of Disturbance Transfer Function And Restricting The Closed Loop Poles To A Desired Sub-Region In S-Plane. An Algorithm For Control Allocation Has Been Proposed To Modify The Weight Matrix Of Weighted-Pseudo-Inverse Allocation In Presence Of Actuator Rate And Position Saturations. The Algorithm Is Found To Be Effective In Allocating The Control Inputs Of A Satellite Launch Vehicle Whose Model Has Been Developed In This Thesis. This Particular Launch Vehicle Has Eight Actuators To Control Three Attitudes. Two Rigid Body Models (One Neglecting Slosh And The Other Including Slosh Dynamics) Are Developed From The Fundamental Equations, So As To Separate Allocation From Controller Design. A Second Algorithm For Allocation Including Actuator Dynamics Is Formulated As A Linear Matrix Inequality Problem And Solved Using Lmi Toolbox Of Matlab. The Algorithm Has Been Successfully Applied For Distributing The Net Control Demand Of A Thrust Vector Controlled Missile System, Where Allocation Neglecting Actuator Dynamics Failed To Track The Given Attitude Command. Disturbance Rejection Controller Designed By Restricting Closed Loop Pole Location Could Satisfy Performance Specification For Small Disturbances, But Degradation Of Performance For Large Disturbances Is Unavoidable. An Existence Condition For Equivalent Input Disturbance (Eid) Is Derived, From Which An Eid Estimator Is Proposed To Modify The Control Law. The Eid Observer Based Controller Is Simple And Easy To Implement, But Its Performance Greatly Depends On The System Parameters And Bandwidth Of The Filter. In Another Approach, The Asymptotic Eid Observer Based Control Law Is Proposed Here To Improve Disturbance Attenuation, Particularly For Low Frequencies. Robustness Of The System Is Analyzed By Estimating A Perturbation Bound To System Parameters For Which The Closed Loop System Remains Stable. The Robust Performance Bound Estimation Establishes That The Performance Improvement Is Achieved Not Only In Terms Of Disturbance Attenuation But Also To System Parameter Perturbations For Which Closed-Loop System Is Robustly Stable.