Upper bound ℋ︁∞and ℋ︁2control for collocated structural systems

Abstract

A static-rate-feedback control for collocated structural systems is considered in this paper. The feedback gain matrix is obtained by solving linear matrix inequalities (LMIs) to minimize an upper bound of the closed-loop ℋ︁∞ or ℋ︁2 norm. The LMI conditions are obtained by assuming the form of Lyapunov matrices in the standard LMI conditions for evaluating the ℋ︁∞ or ℋ︁2 norm. We demonstrate that the obtained upper bounds of the ℋ︁∞ and ℋ︁2 norms closely match their actual values, respectively, when a relatively large amount of energy is allowed for the control. A decentralized rate feedback controller that globally minimizes the upper bound of the closed-loop ℋ︁∞ or ℋ︁2 norm can also be obtained with the proposed framework. Furthermore, if the coefficient matrices of the system's equations of motion are linear functions of structural design parameters, the obtained result for the controller synthesis can be easily extended to an integrated design problem of structural and control systems, a simultaneous optimal design of the structural design parameters and the feedback controller, while retaining the LMI structure with respect to the feedback gain matrix and structural design parameters. This fact means that the global optimal solution to the integrated design problem, which is generally hard to solve in a global sense, can be obtained if we take the upper bound of the closed-loop norm as the objective function. Copyright © 2008 John Wiley & Sons, Ltd.