Invariants and canonical forms for linear system with delay: Single input case

1984 ◽  
Author(s):  
Stanislaw Zak ◽  
Wu-sheng Lu ◽  
E. Lee
Keyword(s):  
Linear System ◽  
Canonical Forms ◽  
System With Delay ◽  
Single Input

On Closure of a Submodule and a Linear System with Delay

2001 ◽  
Vol 34 (13) ◽  
pp. 461-464
Author(s):  
Sri Wahyuni ◽  
Indah Emilia Wijayanti
Keyword(s):  
Linear System ◽  
System With Delay

Input Requirements and Parametric Errors for System Identification Under Periodic Excitation

1972 ◽  
Vol 94 (4) ◽  
pp. 296-302 ◽  
Author(s):  
L. L. Hoberock ◽  
G. W. Stewart
Keyword(s):  
Linear System ◽  
Input State ◽  
Matrix Elements ◽  
Periodic Excitation ◽  
Input Output ◽  
Input Matrix ◽  
Multiple Input ◽  
Minimum Number ◽  
Single Input ◽  
Work Done

This paper provides the conditions on periodic system excitation necessary for unique identification using a multiple input state model of a dynamic system. Results include the minimum number of input frequencies necessary to uniquely determine all state and input matrix elements of an n dimensional linear system. It is shown that this development encompasses earlier work done on single input-output systems. A technique is provided for predicting parametric errors to be expected from identification under periodic excitation, and several examples are used to illustrate these errors.

Pole Placement for Single-Input Linear System by Proportional-Derivative State Feedback

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Taha H. S. Abdelaziz
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
Pole Placement ◽  
Feedback Gain ◽  
Time Varying ◽  
Placement Problem ◽  
Single Input ◽  
Time Invariant

This paper deals with the direct solution of the pole placement problem for single-input linear systems using proportional-derivative (PD) state feedback. This problem is always solvable for any controllable system. The explicit parametric expressions for the feedback gain controllers are derived which describe the available degrees of freedom offered by PD state feedback. These freedoms are utilized to obtain closed-loop systems with small gains. Its derivation is based on the transformation of linear system into control canonical form by a special coordinate transformation. The solving procedure results into a formula similar to Ackermann’s one. In the present work, both time-invariant and time-varying linear systems are treated. The effectiveness of the proposed method is demonstrated by the simulation examples of both time-invariant and time-varying systems.

Dynamic logarithmic state and control quantization for continuous-time linear systems

Robotica ◽  
2022 ◽  
pp. 1-16
Author(s):  
Jiashuo Wang ◽  
Shuo Pan ◽  
Zhiyu Xi
Keyword(s):  
Feedback Control ◽  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Control Law ◽  
Quantized Feedback ◽  
Single Input ◽  
Simulation Results ◽  
And Control ◽  
Time Linear

Abstract This paper addresses logarithmic quantizers with dynamic sensitivity design for continuous-time linear systems with a quantized feedback control law. The dynamics of state quantization and control quantization sensitivities during “zoom-in”/“zoom-out” stages are proposed. Dwell times of the dynamic sensitivities are co-designed. It is shown that with the proposed algorithm, a single-input continuous-time linear system can be stabilized by quantized feedback control via adopting sensitivity varying algorithm under certain assumptions. Also, the advantage of logarithmic quantization is sustained while achieving stability. Simulation results are provided to verify the theoretical analysis.

Parametric identification of linear systems using AutoRegressive with eXogenous input model expansion on Meixner-like orthonormal bases

2019 ◽  
Vol 42 (2) ◽  
pp. 306-321
Author(s):  
Safa Maraoui ◽  
Kais Bouzrara
Keyword(s):  
Genetic Algorithms ◽  
Linear System ◽  
Linear Systems ◽  
Experimental Research ◽  
Parametric Identification ◽  
New Model ◽  
System With Delay ◽  
Orthonormal Bases ◽  
Bounded Error ◽  
Input Model

This paper proposes a new model for a representation of linear system with delay. This latter, is given by decomposing the coefficients of the AutoRegressive with eXogenous input (ARX) model associated with the output and the input on two independent Meixner-like orthonormal bases. The resulting model is called ARX Meixner-like model. In order to ensure the parameter complexity reduction, the Meixner-like poles are optimized using Genetic algorithms method. Unknown But Bounded Error (UBBE) approaches are used to update the uncertainty domain of the parameters of the new obtained model. A numerical example of system with delay and two examples of experimental research are made to prove the efficiency of the proposed approach.

LINEAR SYSTEM CANONICAL FORMS

1974 ◽  
Vol 1 (3) ◽  
pp. 197-202 ◽  
Author(s):  
JAMES T. CAIN ◽  
WILLIAM G. VOGT ◽  
MARLIN H. MICKLE
Keyword(s):  
Linear System ◽  
Canonical Forms
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