A Behavioral Approach to H Control

The purpose of this talk is to outline an approach to the synthesis of controllers and lters in the behavioral frame work The main advantage is that the results obtained this way are representation independent with all the algorithmic advan tages that this entails The aim is to explain the solution of the problem discussed below but before doing so a number of back ground concepts need to be introduced We have a linear time invariant plant in which to be controlled variables w d z with d exogenous disturbances and z endoge nous to be controlled variables should be regulated by attaching a controller that acts on control variables c The basic control spec i cations are expressed by a quadratic functional jwj S which here equals jdj jzj whose integral needs to be non negative Let P be the plant behavior the behavior of the variables w before the controller is attached and N is the sub behavior compatible with