© 1988 by Institute of Mathematics and its Applications
Partial Singular-Value Assignment in the Design of Robust Observers for Discrete-Time Descriptor Systems
Central Control Department, British Gas plc Coventry Road, Hinckley, Leicestershire LE10 0NA
Mathematics Department, Coventry Polytechnic Priory Street, Coventry CV1 5FB
This paper considers how feedback may be used to affect the singular values of a matrix. The phrase ‘partial singular-value assignment’ refers to the fact that we are able to assign p of the singular values arbitrarily, where p is the dimension of the system output. The remaining n–p singular values, where n is the dimension of the state space, are moved in a predetermined manner. This allows us to maximize the smallest singular value and minimize the largest singular value when using our method on a specific data set. A numerically stable and efficient algorithm is presented which allows the p singular values to be located arbitrarily. We also present an algorithm which tends to achieve an upper bound for the smallest singular value similar to that of our assignment algorithm, and similar matrix conditioning, but which allows us to retain a certain amount of matrix sparsity when this is of importance. This second algorithm is heuristic in nature but appears to give good results in practice. A robust observer for a discrete-time descriptor system is designed which makes use of our algorithms. The observer design has been applied to a high-pressure gas network, and has proved to be successful in practice.