scholarly journals An example of a linear discrete system with unstable Lyapunov exponents

2016 ◽  
Vol 26 (2) ◽  
pp. 169-176
Author(s):  
I.N. Banshchikova ◽  
Keyword(s):  
Lyapunov Exponents ◽  
Discrete System ◽  
Linear Discrete System

scholarly journals On a Decomposition Method in the Problem of Operation Speed for a Linear Discrete System with Bounded Control

2019 ◽  
Vol 09 (4) ◽  
pp. 157-161
Author(s):  
D.N. Ibragimov ◽  
E.E. Turchak
Keyword(s):  
Explicit Form ◽  
Discrete System ◽  
Decomposition Theorem ◽  
Two Dimensional ◽  
State Matrix ◽  
Bounded Control ◽  
Operation Speed ◽  
Linear Discrete System ◽  
Minimum Number ◽  
Main Decomposition

The article presents the problem of operation speed for a linear discrete system with bounded control. For the case when the minimum number of steps necessary for the system to reach zero significantly exceeds the dimension of the phase space, a method of decomposition into scalar and two-dimensional subsystems is developed, based on the reduction of the state matrix to normal Jordan form. Moreover, due to the developed algorithm for adding two polyhedrons with linear complexity, it is possible to construct sets of 0-controllability for two-dimensional subsystems in an explicit form. A description of the main tools for solving the problem of operation speed is also presented, as well as the statement of the decomposition problem. Further, some properties of polyhedrons in the plane are formulated and proved, on the basis of which an algorithm for calculating the set of vertices of the sum of two polyhedrons in R2 in explicit form is developed. In conclusion, the main decomposition theorem is formulated and proved. And on the basis of the developed methods, the solution to the problem of the optimal damping speed of a high-rise structure located in the zone of seismic activity was constructed.

scholarly journals A Simple Method of Identification for Linear Discrete System

1980 ◽  
Vol 16 (1) ◽  
pp. 55-62
Author(s):  
Aisuke KATAYAMA ◽  
Rin'nei WATANABE ◽  
Hideo TAMAMOTO
Keyword(s):  
Discrete System ◽  
Simple Method ◽  
Linear Discrete System

A Simple Iterative Procedure for the Identification of the Unknown Parameters of a Linear Time Varying Discrete System

1963 ◽  
Vol 85 (2) ◽  
pp. 227-235 ◽  
Author(s):  
Harold J. Kushner
Keyword(s):  
Impulse Response ◽  
Discrete System ◽  
Linear Time ◽  
Time Varying ◽  
Unknown Parameters ◽  
Random Drift ◽  
Process Dynamics ◽  
Linear Discrete System ◽  
Single Input ◽  
Time Variations

A new “steepest descent” approach to the “adaptive control system” problem of the determination of the process dynamics of a time varying system is analyzed in considerable detail. The unknown parameters are the parameters of the impulse response of a linear discrete system. The identification procedure is a first-order iterative process and is designed to operate with the natural inputs of the system to be identified. After each new (single) input, new estimates of all the unknown parameters are computed. The method is computationally simple and, in its analysis, the effects of additive noise in the observations (of both input and output), random drift with time, or neglected parameters of the impulse response are handled with relative ease and become transparent. Time variations are taken directly into account, thus eliminating the necessity of the assumption of stationarity over a period of time.

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