SISO Filtering

Abstract

In this chapter we examine the fundamental design trade-offs that apply to linear scalar filtering problems based on bounded error estimators. We will see that, due to the condition of bounded error estimation, the filtering sensitivity functions introduced in the last chapter are necessarily constrained at points in the complex plane determined by ORHP poles and zeros of the plant. These interpolation constraints, in turn, translate into Poisson and Bode-type integral relations, which show essential limitations in the achievable performance, and induce clear trade-offs in filter design.