<p>In many practical multi-channel active sound control (ASC) applications, such as active noise control (ANC), various constraints need to be satisfied, such as the robust stability constraint, noise amplification constraint, controller output power constraints, etc. One way to enforce these constraints is to add a regularization term to the Wiener filter formulation, which, by tuning only a single parameter, can over-satisfy many constraints and degrade the ANC performance. Another approach for non-adaptive ANC filter design that can produce better ANC performance is to directly solve the constrained optimization problem formulated based on the <em>H</em>₂/<em>H</em>_inf control framework. However, such a formulation does not result in a convex optimization problem and its practicality can be limited by the significant computation time required in the solving process. In this dissertation, the traditional <em>H</em>₂/<em>H</em>_inf formulation is convexified and a global minimum is guaranteed. It is then further reformulated into a cone programming formulation and simplified by exploiting the problem structure in its dual form to obtain a more numerically efficient and stable formulation. A warmstarting strategy is also proposed to further reduce the required iterations. Results show that, compared with the traditional methods, the proposed method is more reliable and the computation time can be reduced from the order of days to seconds. When the acoustic feedback path is not strong enough to cause instability, then only constraints that prevent noise amplification outside the desired noise control band are needed. A singular vector filtering method is proposed to maintain satisfactory noise control performance in the desired noise reduction bands while mitigating noise amplification.</p> <p><br></p> <p>The proposed convex conic formulation can be used for a wide range of ASC applications. For example, the improvement in numerical efficiency and stability makes it possible to apply the proposed method to adaptive ANC filter design. Results also show that compared with the conventional constrained adaptive ANC method (leaky FxLMS), the proposed method can achieve a faster convergence rate and better steady-state noise control performance. The proposed conic method can also be used to design the room equalization filter for sound field reproduction and the hear-through filter design for earphones.</p> <p><br></p> <p>Besides efficient filter design methods, efficient filter implementation methods are also developed to reduce real-time computations in implementing designed control filters. A polyphase-structure-based filter design and implementation method is developed for ANC systems that can reduce the computation load for high sampling rate real-time filter implementation but does not introduce an additional time delay. Results show that, compared with various traditional low sampling rate implementations, the proposed method can significantly improve the noise control performance. Compared with the non-polyphase high-sampling rate method, the real-time computations that increase with the sampling rate are improved from quadratically to linearly. Another efficient filter implementation method is to use the infinite impulse response (IIR) filter structure instead of the finite impulse response (FIR) filter structure. A stable IIR filter design approach that does not need the computation and relocation of poles is improved to be applicable in the ANC applications. The result demonstrated that the proposed method can achieve better fitting accuracy and noise control performance in high-order applications.</p>