Unfolding the zero structure of a linear control system Original Research Article

This paper is motivated by the problem of controller design for a parameter-dependent linear system. Many compensation techniques depend critically on aspects of the zero structure of the system, such as relative degree, or the nonminimum-phase property. However, the zero structure is structurally unstable, meaning it may change discontinuously with small changes in the parameters. Thus it is crucial that the designer know what structures and structural transitions are possible. This paper uses a miniversal deformation, or unfolding, of the Kronecker form previously reported by the authors, and applies it directly to pencils in a canonical form of the system matrix. The unfolding is used to explore all zero structures in the neighborhood of a nominal system. Several examples are presented. When possible, the results are presented in the form of a bifurcation diagram.