A Canonical Parameter Space for Linear Systems Design

A canonical parameter space is introduced for linear time-invariant, discrete-time systems design. All observable and controllable linear systems of a given order are shown to share one stability domain in this space. This invariance of the stability domain is shown to be fundamental to the solution of the gain output-feedback stabilizability problem and other significant linear systems design problems. The geometric properties of the stability domain are investigated. Its convex hull is shown to be a simplex. Our approach is compared to the D-decomposition, the root-locus, and other methods. Its advantages over these methods in attacking the problem of stabilizability by gain output-feedback and other important problems are discussed.