Qualimetry of reachability and response of linear dynamic systems

Abstract

The paper considers some existing numerical estimations of controllability and reacability; their disadvantages are stated from the point of view of application of these estimations to solve the control system synthesis tasks. The existing indices do not take into account the compromise character of requirements to the control systems which include not only a good control response attack but weak dynamic response as well. To estimate these features it is necessary to use different quantitative and structural indices which reflect the interaction of external effects and system reactions. The author has proposed to form on the basis of gramians of controllability and reachability two types of «input-state» quantitative indices from the terminal control tasks and the tasks of synthesizing weak-pertubable systems. The similar approach may be implemented as well on the basis of structural characteristic application.

Keywords

• quantitative analysis
• controllability
• linear dynamic systems
• Hessenberg representation
• controllability measures
• structural indices