scholarly journals Stability Analysis of Multi-Dimensional Linear Time Invariant Discrete Systems within the Unity Shifted Unit Circle

2016 ◽  
Vol 07 (06) ◽  
pp. 709-717 ◽  
Author(s):  
P. Ramesh
Keyword(s):  
Stability Analysis ◽  
Unit Circle ◽  
Linear Time ◽  
Discrete Systems ◽  
Linear Time Invariant ◽  
Time Invariant

Stabilization and Optimal Quadratic Regulation of Linear Time-Invariant Discrete Systems with Data Dropout Compensation

2013 ◽  
Vol 816-817 ◽  
pp. 574-582
Author(s):  
Manuel de La Sen ◽  
S. Alonso-Quesada ◽  
A. Ibeas
Keyword(s):  
Linear Time ◽  
Finite Size ◽  
Discrete Systems ◽  
Memory Storage ◽  
Control Structures ◽  
Global Asymptotic Stabilization ◽  
Linear Time Invariant ◽  
Transmission Errors ◽  
Remote Controller ◽  
Time Invariant

This paper discusses the global asymptotic stabilization and least-squares optimal control for a linear system with potential transmission errors subject to Bernouilli statistics from a remote controller to the actuator. The controlled system is able to compensate certain missed data through the use of finite size fixed memory storage arrays which store the last valid data which has been transmitted so as to replace the current missed one in the control structures.

scholarly journals Modified Schur-Cohn Criterion for Stability of Delayed Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Ignacio Mulero-Martínez
Keyword(s):  
Linear Time ◽  
Discrete Systems ◽  
Delayed Systems ◽  
Triangular Matrices ◽  
Numerical Errors ◽  
Real Roots ◽  
Linear Time Invariant ◽  
Alternative Approach ◽  
Linear Time Invariant Systems ◽  
Time Invariant

A modified Schur-Cohn criterion for time-delay linear time-invariant systems is derived. The classical Schur-Cohn criterion has two main drawbacks; namely, (i) the dimension of the Schur-Cohn matrix generates some round-off errors eventually resulting in a polynomial ofswith erroneous coefficients and (ii) imaginary roots are very hard to detect when numerical errors creep in. In contrast to the classical Schur-Cohn criterion an alternative approach is proposed in this paper which is based on the application of triangular matrices over a polynomial ring in a similar way as in the Jury test of stability for discrete systems. The advantages of the proposed approach are that it halves the dimension of the polynomial and it only requires seeking real roots, making this modified criterion comparable to the Rekasius substitution criterion.

scholarly journals Stability Analysis of Linear Feedback Systems in Control

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1518
Author(s):  
Mutti-Ur Rehman ◽  
Jehad Alzabut ◽  
Muhammad Fazeel Anwar
Keyword(s):  
System Theory ◽  
Stability Analysis ◽  
Linear Time ◽  
Singular Values ◽  
Low Rank ◽  
Gradient System ◽  
Feedback Systems ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

This article presents a stability analysis of linear time invariant systems arising in system theory. The computation of upper bounds of structured singular values confer the stability analysis, robustness and performance of feedback systems in system theory. The computation of the bounds of structured singular values of Toeplitz and symmetric Toeplitz matrices for linear time invariant systems is presented by means of low rank ordinary differential equations (ODE’s) based methodology. The proposed methodology is based upon the inner-outer algorithm. The inner algorithm constructs and solves a gradient system of ODE’s while the outer algorithm adjusts the perturbation level with fast Newton’s iteration. The comparison of bounds of structured singular values approximated by low rank ODE’s based methodology results tighter bounds when compared with well-known MATLAB routine mussv, available in MATLAB control toolbox.

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