It is well-known that feedback can be introduced to stabilize an unstable system, to attenuate the response of a system to disturbance, and to reduce the effect of plant parameter variations and modeling error. On the other hand, feedback design is also known to be contingent on various performance considerations and physical constraints, which invariably impose limitations on the achievable performance and necessitate tradeoffs among conflicting design objectives. An important step in the feedback design process, therefore, is to analyze how system properties may inherently impose constraints upon design and thus may fundamentally limit the performance attainable. In this talk I shall present a control theorist’s perspective into this intriguing area of scientific inquiry, from the early triumph of feedback theory to the latest development in networked control. The talk will begin with a tutorial review of Bode's classical integral relations, widely considered a pillar of feedback theory. This will then usher in the more recent progress, of which multivariable integral relations of Bode and Poisson type, and a number of canonical optimal control problems will constitute the primary theme. Interpretations of these results from control perspectives will be particularly emphasized. The talk will focus on multivariable systems and address a number of new, unique issues only found in multivariable systems, with a particular undertone to networked control systems.
