Title: On the Lyapunov-Based Approach to Robustness Bounds Redacted for Privacy

The objective of this investigation is the development of improved techniques for the estimation of robustness for dynamic systems with structured uncertainties, a problem which was approached by application of the Lyapunov direct method. This thesis considers the sign properties of the Lyapunov function derivative integrated along finite inter-vals of time, in place of the traditional method of the sign properties of the derivative itself. This proposed approach relaxes the sufficient condi-tions of stability, and is used to generate techniques for the robust design of control systems with structured per-turbations. The need for such techniques has been demon-strated by recent research interest in the area of robust control design. The system considered is assumed to be nominally lin-ear, with time-variant, nonlinear bounded perturbations. Application of the proposed technique warrants that esti-mates of robustness will either match or constitute an im-provement upon those obtained by application of the tradi-tional Lyapunov approach. The application of numerical procedures are used to demonstrate improvements in estima-tions of robustness for two-, three- and four-dimensional dynamic systems with one or more structured perturbations. The proposed numerical approaches obtain improved bounds, which are considered in the sense of their engineering as-pects. To increase the accuracy of the numerical proce-dures, symbolic algebraic calculations are utilized