Integrated structural and control design for vector second-order systems via LMIs

Iterative redesign techniques are proposed to integrate the design of the structural parameters and the active control parameters for vector second-order lumped-parameter structural systems. The objective is to minimize the required active control effort to satisfy given output variance constraints and robust performance constraints. The problem is formulated as an iterative sequential control design followed by control/structure redesign. Each step of the iterative algorithm is formulated as a Linear Matrix Inequality (LMI) optimization problem that can be solved effectively using available LMI solvers. Convergence of the proposed algorithm to a solution that provides improved control effort and robust stability compared to the single-step structural and control design is guaranteed. Both static state-feedback and dynamic output feedback problems are considered.