Qualitative Robustness and Its Role in the Robust Control of Uncertain Engineering Systems

This paper addresses the issue of robustness of linear uncertain systems. In addition to the conventional notion of robustness based on quantitative information, in this paper, a new and novel perspective of qualitative robustness is introduced. The qualitative robustness measure is inspired by ecological principles and is based on the nature of interactions and interconnections of the system. Thus, using the proposed framework, the robustness of engineering systems can be assessed both from quantitative as well as qualitative information. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts it is shown that a specific quantitative set of matrices labeled ‘Target Sign Stable Matrices’ are the best nominal matrices. These concepts are then extended to closed loop control systems and problem of control design and for ease in design a new set of matrices ‘Target Pseudosymmetric Matrices’ are introduced which enhance the class of desirable closed loop system matrices. Examples are included to illustrate these concepts.