Design procedure for modal controllers for defective and nearly defective systems

This paper presents a procedure for designing feedback controllers for defective systems with repeated eigenvalues, and also for a nearly defective system with close eigenvalues. For the nearly defective system, we first transform it into a defective one, and then apply the same method to deal with the nearly defective system. A method for computing the gain matrices is discussed here. The methodologies proposed are based on the modal coordinate equation to avoid the tedious mathematical manipulation. As an application of the present procedure, a numerical example is given.