Robustness analysis of uncertain time-delay systems

This thesis examines how integral quadratic constraints (IQC's) can be used in robustness analysis for feedback systems with time-delay uncertainty. The main advantage of stability analysis of time-delay systems via IQC approach is that the results can be readily extended to the cases with additional uncertainties.; First, the thesis provides a result concerning robust stability of uncertain time-delay systems with IQC-bounded uncertainties such as conic nonlinearities, real/complex parameter uncertainty and so on. A new delay-dependent state-space stability criterion is formulated in the form of easily checked linear matrix inequality (LMI) condition. Two applications of the main result are presented, one with only time-delay uncertainty and one with both time-delay and parameter uncertainty. Conservativeness of the result is discussed by comparing with other results through examples and Monte Carlo simulation.; Next, the thesis describes a set of delay-dependent IQC's for time-delay uncertainty. The set is linearly parameterized in terms of the frequency response of a complex matrix-valued multiplier. Using LMI optimization techniques, one may compute optimal multipliers and thereby obtain less conservative IQC stability robustness bounds for systems with uncertain time-delays. It is shown that existing IQC's for time-delay uncertainty correspond to particular choices for the multiplier. The thesis also provides an appropriate parameterization of time-delay uncertainty that is crucial in application of IQC theory for stability analysis. Conservativeness of the proposed parameterized IQC's is discussed.; Finally, the thesis proposes a method to test the stability of time-delay systems without frequency gridding. In deriving the result, a general sector transformation is given that is parameterized by a scalar function with phase constraints. The result is a delay-dependent stability criterion consisting of a set of non-frequency dependent LMI's. The LMI conditions are derived by applying the finite-frequency positive-realness condition.