This thesis addresses the problem of integrated mechanical structure and control system design problem, while a set of n closed-loop performance specifications are required to be satisfied simultaneously. The traditional method of solving the integrated design problem is by simultaneous optimization of both mechanical structure parameters and control gains, with respect to a fixed controller structure. Based on this frame of optimization, the integrated design approach is mathematically compared with its counterpart — the sequential design approach. The comparison leads to two important conclusions in this thesis, as why and when should the integrated design approach be applied.

However, the optimization method to solve the integrated design problem is hard to perform since nonconvex optimization problems are always need to be solved. Hence, in this thesis, a new integrated design method referred to as the Convex Integrated Design (CID) method, is proposed when all closed-loop performance specifications are convex with respect to the closed-loop transfer matrix. By making use of the convexity of the closed-loop performance specifications, the CID problem is solved with a simple three-stage CID algorithm. The main strength of the CID method lies in the first two stages of the CID algorithm. In the first stage, a set of n sample systems are found so that each closed-loop specification is satisfied by at least one sample system. Then, these sample systems are combined through a "convex combination" process, and it is proved that the resultant closed-loop system satisfies the set of n specifications simultaneously. This design strategy lessens much of the burden on the designer, when he/she only needs to focus on finding sample system to meet one of the multiple specifications at each time. Then in the third stage, through the solution of an equality-constrained optimization problem, the design parameters, i.e., the mechanical structure parameters and the controller, are uniquely determined, and the closed-loop performance beyond that defined by the set of performance specifications is obtained. This CID method is straightforward and easily implemented. Its effectiveness is verified in the design of a linear positioning system, a semi-active suspension system and a planar parallel manipulator in this thesis.