The first significant results in the theory of equations (4) were obtained in [[#References|[11]]], where an effective
...dity of the majority of results listed above has also been established for systems of equations of type (4); however, in contrast to the case of a single equa
32 KB (4,357 words) - 17:14, 7 February 2011
...f [[Orbit stability|orbit stability]] of closed trajectories of autonomous systems of differential equations one has to apply necessary and sufficient conditi
...">[10]</TD> <TD valign="top"> E. Jury, "Inners and stability of dynamic systems" , Wiley (1974)</TD></TR></table>
9 KB (1,283 words) - 14:55, 7 June 2020
...ed space]]), in problems concerning the extension of functions, and in the theory of differential equations.
In optimization over a finite or infinite horizon, e.g. in the theory of optimal economic growth, one aims to maximize a future return function
5 KB (752 words) - 08:29, 6 June 2020
A code intended for the control of the functioning of an adder. When adding numbers represented in the bina
...rror-correcting code|Error-correcting code]]). In the study of problems of control of an adder one usually considers an encoding $ f: \{ 0 \dots M - 1 \} \
8 KB (1,189 words) - 09:46, 26 March 2023
...ems, in particular, in circuit theory [[#References|[a4]]] and for control theory problems involving an $ H ^ \infty $-
...[[#References|[a1]]]. Generalizations of the Nevanlinna–Pick interpolation theory have also been developed for functions of several variables (see [[#Referen
10 KB (1,474 words) - 14:54, 7 June 2020
are obtained in a less general form than for single-server systems, and are connected with a condition on the existence of so-called renewal e
must be satisfied. If for such systems, in triangular arrays, the distributions of $ \tau _ {j} ^ {(n)} e $
18 KB (2,750 words) - 19:29, 16 January 2024
...ces|[a21]]], [[#References|[a22]]] for general surveys of linear filtering theory.
...metrization, and this has led to extensive research on characterizing such systems and exploring the connection, uncovered by R.W. Brockett and J.M.C. Clark [
15 KB (2,302 words) - 08:03, 21 January 2024
...s generalizations and modifications which reflect various features of real systems. In the case of a finite automaton $ (A, S, B, \phi , \psi ) $
..., algebraic theory of|Automata, algebraic theory of]]); problems in coding theory generate the concepts of self-regulating automata, reversible automata, etc
18 KB (2,794 words) - 10:01, 25 April 2020
...rcuit is one of the first classes of control systems (cf. [[Control system|Control system]]) considered from the mathematical point of view, as well as one of
...valign="top"> V.I. Shestakov, "On a logical calculus applicable to the theory of relay-contact circuits" ''Uchen. Zap. Moskov. Gosudarstv. Univ. Mat.''
8 KB (1,204 words) - 01:44, 5 March 2022
...te evolution of the process is observed by the controller. A corresponding
theory has also been developed in the case of partial observations (incomplete dat
...w.encyclopediaofmath.org/legacyimages/c/c026/c026010/c02601030.png" /> and
control action <img align="absmiddle" border="0" src="https://www.encyclopediaofmat
107 KB (14,649 words) - 21:43, 15 December 2020
...of finite-dimensional vector spaces, fields, algebraic systems, functional systems, etc.) which is independent of the particular computer used and which may b
...arious programming methods. A computational algorithm contains a number of control parameters, which remain indefinite in the first part, form a fixed part of
10 KB (1,642 words) - 08:41, 29 August 2014
...bjects, such as complex spaces, topological manifolds, algebras, etc. Such systems occur in may parts of mathematics both as tools and as objects to be invest
parameter systems of smooth curves $ \{ \sigma ^ {1} \dots \sigma ^ {n} \} $
20 KB (3,056 words) - 08:25, 6 June 2020
...(from their own specific standpoints). By revealing the general aspects in systems of such different nature, cybernetics provides a general and moreover new m
In many specific cybernetic systems, time is regarded as a parameter taking only a discrete set of values (usua
35 KB (5,424 words) - 11:17, 26 March 2023
...cal systems with discrete states and changes of states called events; such systems arise e.g. in digital network communication protocols.
...l calculus" D. Franke (ed.) F. Kraus (ed.) , ''Design Methods of Control Systems'' , '''2''' , Pergamon (1991) pp. 723–728</TD></TR></table>
8 KB (1,166 words) - 06:28, 30 May 2020
In control theory one studies equations $ \dot{x} = f( x, u) $
with a control parameter $ u $;
11 KB (1,659 words) - 05:14, 24 February 2022
...[[Krein space|Krein space]]). The results are used in [[H^infinity-control-theory| $ H ^ \infty $
control theory]] (see [[#References|[a8]]]), and when the data are Fourier coefficients of
11 KB (1,460 words) - 14:32, 7 June 2020
...uters and of programming them relies, to a large extent, on ideas from the theory of algorithms and mathematical cybernetics. In turn, practical work with co
Common to all abstract machines is the presence of a finite control device that may be in one of the states $ q _ {1} \dots q _ {k} $.
18 KB (2,656 words) - 04:11, 6 June 2020
The modern theory of linear inequalities has been constructed on the basis of this generaliza
...onomic technology and economic planning reduce to the solution of specific systems of linear inequalities; this has significantly determined the modern trend
14 KB (2,052 words) - 10:49, 21 March 2022
...rators which is one of the most important classes of operators in function theory; it has many applications in different fields of mathematics and applied ma
...Hankel operators. The following realization is very important in function theory. Given a function $\phi \in L ^ { \infty }$, one defines the Hankel operato
18 KB (2,757 words) - 00:48, 15 February 2024
...ts. Actually, Wold introduced (a1) as a joint representation for AR and MA systems (cf. also [[Mixed autoregressive moving-average process|Mixed autoregressiv
...esponding to stable and miniphase ARMA or (finite-dimensional) state space systems is by far the most important one. In this case there is a wide class of ide
9 KB (1,297 words) - 09:30, 3 February 2024