SOME GENERALIZATIONS IN SYSTEM THEORY AND THEIR APPLICATIONS TO CONTROL SYSTEMS,
Abstract
Some definitions of the concepts 'state' and 'state-deterministic system' have been given by L. A. Zadeh and C. A. Desoer in their book 'Linear System Theory: The State Space Approach'. In this thesis, using some of their ideas such as physical systems and their measurable attributes, a more fundamental definition of a 'system' is given. Two new concepts, namely, 'functional dependence' and 'quasi-functional dependence' between attribute sets, are introduced, by means of which the concepts of output, input, and state, attribute sets are defined. Comparison of systems in two ways, in terms of their 'index sets' and in terms of their 'attributes sets,' is used to clarify the concepts of 'extensionally-state-determined' and 'extensionally-state-stochastic' systems. The concept of 'versatility of a system' is next introduced to provide a third way of comparing two systems. It is shown that if a linear control system is less versatile than another, it is as versatile as the latter system provided with a suitable linear feedback and with the system matrix same as that of the first. Two theorems are proved regarding the versatility of linear free systems. A new perturbation process, called 'brief perturbation process' here, which can be applied to control systems, is described in detail. Next, an interesting connection between uncontrollability and optimality is pointed out and the well-known sufficient conditions for controllability of a linear time-invariant control system are derived. Finally, a new definition of impulse response for linear as well as nonlinear control systems, using the concept of a brief perturbation process, is given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1967
- Accession Number
- AD0653524
Entities
People
- Sadanand D. Agashe
Organizations
- University of Illinois Urbana–Champaign