Robustness measures for linear time-invariant time-delay systems

grantor: University of TorontoTime delays which occur between the inputs and outputs of physical systems are often found in industrial systems, and the presence of such time-delay makes the design of feedback controllers for a system more demanding, since time-delay may tend to destabilize a system. This thesis studies robust measures for characterizing such time-delay systems; in particular, it studies stability robustness of and controllability/stabilizability robustness of linear time-delay systems. The first part of the thesis, analyzes the stability robustness of two types of objects: (1) quasipolynomials, and (2) matrices for linear time-invariant time-delay systems of the retarded and neutral type. In the case of (1), we consider quasipolynomials with affine uncertainties. A general solution for this problem is then obtained by using tools from convex analysis. In the case of (2), we consider a system described by a stable state space model, and we define the real stability radius of a stable system as being the distance of the perturbed system matrix to the set of unstable systems. The results obtained extend the real stability radius for linear time-invariant finite dimensional systems to the case of linear time-invariant infinite dimensional systems. The second part of the thesis, deals with controllability/stabilizability robustness of linear time-invariant finite dimensional systems and spectral controllability/stabilizability robustness of linear time-invariant infinite dimensional systems. We define the real controllablity radius and the real stabilizability radius as being the distance from the nominal system matrix to the set of uncontrollable matrices, and the set of unstabilizable matrices, respectively. The method of solutions for these problems is carried out based on matrix perturbation theory. A number of examples and application studies are included in the thesis to illustrate the type of results which may be obtained.Ph.D