This report pertains to a class of non-linear controllers designed by the Second Method of Lyapunov for the model-reference control of non-linear, time-variable single-input, single output system. In idealized form, these controllers guarantee asymptotic stability of the system by means of corrective feedback generated by a nonlinear switching element whose argument is a linear combination of the states of the system. In this report, necessary and sufficient conditions are obtained for boundedness of the imperfect control that results when switching is non-ideal due to physical implementation or the use of an approximating function which may exhibit dead-zone, hysteresis, saturation or finite switching time, or when state measurement is hampered by noise, transducer error or finite delay. It is shown that in idealized form, the controllers considered approach the switching hyperplane monotonically. This fact which suggests the use of a semi-definite rather than definite Lyapunov function in the synthesis technique is shown to have several advantages over the conventional technique, is used to extend the existence development to the point that calculation of an estimate of the bound is possible. A general analog computer technique is outlined for estimating, the bound and by examples this estimate is found to be realistic. The technique involves calculation of the reachable set of an nth-order linear, time invariant system, not heretofore found in the literature. The development is first presented for an nth-order canonic system. Extension is then made to other forms and limitations are outlined.