Guaranteed convergence ratio of systems with time-varying uncertainties

When the system is subject to possibly fast time varying uncertainties, there does not appear to be similar constraints discussed in the literature. This paper discusses one possible constraints of this type: a certain proportion of state change rate must be used for state convergence. When the uncertainty is absent, this constraint is equivalent to constraining the poles of the system to be within some circle with damping ratio at least at some specified value. The criterion is formulated in the form of a matrix inequality. This criterion can often be combined with other constraints expressible in the form of LMI or BMI without significantly complicating the numerical procedure. The state feedback control problem is also discussed