This article demonstrates a combined ${\mathcal{H}}_{\infty }$ feedback control design for linear time-invariant and linear parameter-varying systems and optimal sensors and actuator selection. The combined design problem is systematically constructed as a mixed Boolean semidefinite programming optimization problem. We impose Big-M reformulations to the non-deterministic polynomial-time-hard coupled problem to be solved as a convex optimization problem using the branch and bound algorithm. The combined design of dynamic output feedback control along with optimal actuator selection for a linear time-invariant seismic rejection controller design serves as an application for validation by simulation. In addition, active vibration control of a smart composite plate along with optimal sensor and actuator selection validates the developed approach for linear parameter-varying controller synthesis. On comparing this approach with exhaustive search, it is observed that mixed Boolean semidefinite programming approaches have faster computation time, and comparing with the iterative reweighted ℓ₁ norm algorithm and mixed Boolean semidefinite programming using outer approximations, mixed Boolean semidefinite programming yields a global solution.

本文展示了一个综合 ${\mathcal{H}}_{\infty }$线性时不变和线性参数变化系统的反馈控制设计，以及最佳传感器和执行器选择。组合设计问题被系统地构造为混合布尔半定规划优化问题。我们对使用分支定界算法作为凸优化问题解决的不确定性多项式-时间-硬耦合问题强加了Big-M格式。动态输出反馈控制与线性时不变抗震控制器设计的最佳执行器选择的组合设计可作为通过仿真进行验证的应用。此外，智能复合板的主动振动控制以及最佳的传感器和执行器选择，验证了线性参数变化控制器综合的开发方法。nor ₁范数算法和使用外部逼近的混合布尔半定规划，混合布尔半定规划产生了全局解。