Applications of the Multivariable Popov Criterion†

Abstract

Two classes of systems are considered for the application of the multivariable Popov criterion. The first is obtained from a linear, finite-dimensional system with a state feedback law derived from a quadratic loss function minimization problem. It is shown that a non-critical part of the system is the set of transducers producing the inputs to the system, in the sense that stability is retained even when the transducers are far from ideal. The second class of systems is derived from linear, finite-dimensional systems which are stable. It is shown that it is always it is possible to tolerate in general a small amount of non-linearity at virtually any point in the system without impairment of stability.