Feedback gain optimization in decentralized eigenvalue assignment

Abstract

This paper develops a new design procedure for minimizing the norm of a decentralized output feedback matrix which assigns a user specified set of eigenvalues. Two distinct approaches which can be meshed together as a unified design tool are derived. Assuming one has computed a decentralized feedback matrix which assigns a desired spectrum, the first approach describes an iterative algorithm which reduces an algebraic cost function (e.g. the Frobenius norm) of the feedback gains while maintaining the desired spectrum. This algorithm allows for small movements in the eigenvalues. The iteration step is based on the first order variational behaviour of the eigenvalue-eigenvector equations. The second algorithm modifies a continuation method for decentralized eigenvalue assignment to include an optimizing factor. Numerical considerations for the design procedures are discussed. An example showing the improvement possible by the application of the procedure is also given.