# Accession Number:

## AD0653524

# Title:

## SOME GENERALIZATIONS IN SYSTEM THEORY AND THEIR APPLICATIONS TO CONTROL SYSTEMS,

# Descriptive Note:

# Corporate Author:

## ILLINOIS UNIV URBANA COORDINATED SCIENCE LAB

# Personal Author(s):

# Report Date:

## 1967-05-01

# Pagination or Media Count:

## 135.0

# 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

# Descriptors:

# Subject Categories:

- Statistics and Probability