Stabilizing controllers for uncertain linear systems with additive disturbances

This paper is concerned with the problem of designing stabilizing controllers for linear systems containing uncertainty. The uncertainty is time-varying with values lying in a specified set and enters through the system matrix, through the input connection matrix and additively. A method is presented for obtaining a linear, state feedback controller which guarantees that the system response ultimately lies in a prespecified neighbourhood of the origin. In some situations, this neighbourhood can be made arbitrarily small and practical stability is achieved. The solution of an algebraic Riccati equation is used to generate the feedback gains for the linear controller. Several examples are included to illustrate the application of the method.