Linear system optimisation with prescribed degree of stability

Abstract

The paper presents a scheme for obtaining a linear-feedback law for a linear system as a result of, minimising a quadratic-performance index; the resulting closed-loop system has the property that all its poles lie in a halfplane Re (s) < − α, where α > 0 may be chosen by the designer. The advantages of this arrangement over conventional optimal design are considered. In particular, it is shown that the reduction of trajectory sensitivity to plant-parameter variations as a result of any closed-loop control is greater for α > 0 than for α = 0, that there is inherently a greater margin for tolerance of time delay in the closed loop when α > 0, that there is greater tolerance of nonlinearity when α > 0, and that asymptotically stable bang-bang control may be achieved simply by inserting a relay in the closed loop when α > 0. The disadvantage of the scheme appears to be that, with α > 0, more severe requirements are put on the power level at which input transducers should operate than for α = 0.