Constraints on sensitivity characteristics in linear multivariable discrete-time control systems

Abstract

This paper is concerned with the limitations on the sensitivity characteristics for linear multivariable discrete-time control systems. Some integral-type constraints and the lower bounds of the weighted H ∞-norm imposed by the unstable poles, the unstable zeros, and their directions of the open-loop system or the given plant are developed by a factorization approach. These constraints and bounds, which are tighter than those in the previous work, are also characterized by the state-space representations. The descriptions are closely related to a special type of the algebraic Riccati equation, and the relation between the sampling period and the sensitivity performance is discussed for digital control systems. The constraints on the more general function (mixed sensitivity function) are investigated in a similar way.