Abstract
The absolute stability of a discrete-time system that can be modeled using a linear time invariant plant in the forward path and a memoryless nonlinear element in the feedback path is investigated. Stability robustness due to various forms of uncertainties is studied.Sufficient conditions for the absolute stability is investigated for the case where the linear part is fixed. A sufficient condition which is more general than any previously reported criterion is found by constructing a Lyapunov function for the case where the nonlinearity is monotonic and conic-sector bounded. This criterion is used to prove an improved sufficient condition for systems with slope-restricted nonlinearities. This criterion is posed as a linear matrix inequality which enables it to be verified efficiently using a computer.Stability robustness due to both parametric and nonparametric uncertainties in the linear time invariant part is also studied. Various stability criteria applicable to systems with fixed linear plants are extended to obtain robust versions applicable to systems with uncertain linear parts. More appropriate uncertainty structures are also proposed for both cases.Stability robustness due to both time-invariant and time-variant delay in the feedback path is investigated. For the time invariant case a method is introduced to find the maximum delay that guarantees stability. For the time-variant case state space models for different types of time variant delays are proposed. Based on these models a criterion for stability in a mean square sense is developed.A discrete time model is developed for a rate control scheme in a computer networking environment based on the models for time-variant delays. A rate control scheme is proposed for the model and an optimal controller synthesis procedure is developed.