# Mathematical description of linear dynamical systems

@article{Klmn1963MathematicalDO, title={Mathematical description of linear dynamical systems}, author={Rudolf E. K{\'a}lm{\'a}n}, journal={Journal of The Society for Industrial and Applied Mathematics, Series A: Control}, year={1963}, volume={1}, pages={152-192} }

There are two different ways of describing uynamicu systems: (i) bymeans of state variables and (ii) by input/output relations. The first method may be regarded as an axiornatization of Newton’s laws of mechanics and is taken to be the basic definition of a system.It is then shown (in the linear case) that the input/output relations determine only one part of a system, that which is completely observable and completely controllable. Using the theory of controllability and observability, methods… Expand

#### 1,418 Citations

Interactions in Linear Dynamical Systems, I

- Computer Science, Mathematics
- Inf. Control.
- 1971

A methodology for the analysis of interacting linear time-invariant dynamical systems is developed and described and its application to interaction analysis of time-variant linear systems and nonlinear systems as well as to synthesis problems is presented. Expand

Feedback realizations in linear multivariable systems

- Computer Science, Mathematics
- 1976

It is shown that redundancy in a feedback system can be expressed as a partial reduction with respect to controllability and observability and this leads to a nice formalism for internally stable control synthesis using rational matrices. Expand

Poles, zeros, and feedback: State space interpretation

- Mathematics
- 1965

This paper is concerned with the relationships between time and frequency domain descriptions of linear, time-invariant systems and with the evaluation of the effects of feedback on such systems. A… Expand

Matrices, polynomials, and linear time-variant systems

- Mathematics
- 1973

Some recent developments in the applications of matrices to problems arising in linear systems theory are described. It is shown how companion form matrices can be used to provide a unified framework… Expand

8 Realization Theory and Algorithms 8

- 2007

In this chapter the following problem is being addressed: Given an external description of a linear system, specifically, its transfer function or its impulse response, determine an internal,… Expand

Finite Dimensional Linear Stochastic System Identification

- 1991

The use of state space systems to represent dynamical systems of various types has a long history in mathematics and physics. Two fundamental examples are the well-known methods for analysing high… Expand

On the Extensions of Kalman’s Canonical Structure Theorem

- Mathematics
- 1991

One of Kalman’s most relevant contributions to system and control theory has been the development of a rigorous conceptual framework in which the relations between external (input-output) and… Expand

On the control of linear multiple input-output systems

- Mathematics
- 1971

The control of linear time-invariant systems is one of the most basic problems of modern automatic control theory. Although “optimal controllers” which minimize certain costs associated with control… Expand

A Local Characterization of Observability

- Computer Science, Mathematics
- 1996

The main results are local characterizations of observability and strong observability (or observability with unknown inputs) of A, C, and (A, B, C) and a generalized product rule for the differentiation of a product of matrices, where only one factor and the product itself are known to be differentiable. Expand

Synthesis and Analysis of Nonlinear Control Systems Based on Transformations and Factorizations

- Mathematics
- 2001

Many real-world systems are inherently nonlinear by nature, hence it is of great benefit to develop control techniques for general nonlinear systems. In this thesis, we will investigate two specific… Expand

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