QUANTITATIVE MEASURES OF MODAL CONTROLLABILITY AND OBSERVABILITY IN VIBRATION CONTROL OF DEFECTIVE AND NEAR-DEFECTIVE SYSTEMS

In this paper, we focus on the control problem of defective systems with repeated eigenvalues. Using the singular-value decomposition of input matrix B and output matrix C in the modal subspace, the quantitative measures of modal controllability and observability of defective systems are discussed. For a near-defective system with close eigenvalues, we first transform it into a defective one, and then apply the same method to deal with near-defective systems. Numerical examples for a general damping system and an airfoil are given to illustrate the applications of the present method.