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.
Affiliation:City University of Hong Kong
Position:Chapter Activities Chair; Distinguished Lecturer
Distinguished Lecture Program
Talk Title: Control Performance Limitation: A Revisit in the Information Age
Talk Title: When is a time-delay system stable and stabilizable?
A time-delay system may or may not be stable for different lengths of delay, and further, may or may not be stabilized via feedback. When will then a delay system be stable or unstable, and for what intervals of delay? What will be the largest range of delay that a feedback system can tolerate? Fundamental questions of this kind have long eluded engineers and mathematicians alike, yet ceaselessly invite new thoughts and solutions. In this talk I shall present an analytical tool that answers to these questions, seeking to provide exact and efficient computational solutions to stability and stabilization problems of time-delay systems. The approach consists of the development of eigenvalue perturbation series and intrinsic delay bounds for stabilization. The former seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix functions or operators. When applied to stability problems, the essential issue dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis, that is, on how the imaginary eigenvalues may vary with respect to the varying parameter. This behavior determines whether the imaginary eigenvalues cross from one half plane into another, and hence plays a critical role in determining the stability of such systems. The latter characterizes analytically the largest range of delay for which a system can be stabilized by a feedback controller. These results depart from the currently pervasive, typically LMI conditions, and yet are conceptually appealing and computationally efficient, requiring only the solution of a generalized eigenvalue problem.