Graphical Abstract Figure
Abstract
This work brings forward several interesting facts about system properties of linear time-invariant discrete-time systems like output controllability, state controllability and state observability, trackability, and input and state observability. Particularly, the work brings about the inter-relationships between these properties while taking a state-space formulation-based approach to come up with simple facts that are backed up by proofs using preliminary linear algebra.
References
1.
Palanthandalam-Madapusi
, H. J.
, and Bernstein
, D. S.
, 2007
, “Unbiased Minimum-Variance Filtering for Input Reconstruction
,” American Control Conference
, New York City
, July 11–13
, IEEE, pp. 5712
–5717
.2.
Kadam
, S. D.
, and Palanthandalam-Madapusi
, H. J.
, 2022
, “Trackability for Discrete-Time Linear Time-Invariant Systems: a Brief Review and New Insights
,” ASME J. Dyn. Syst. Meas. Control
, 144
(3
), p. 031007
. 3.
Kadam
, S. D.
, and Palanthandalam-Madapusi
, H. J.
, 2017
, “Revisiting Trackability for Linear Time-Invariant Systems
,” American Control Conference
, Seattle, WA
, May 24–26
, IEEE, pp. 1728
–1733
.4.
Sain
, M.
, and Massey
, J.
, 1969
, “Invertibility of Linear Time-Invariant Dynamical Systems
,” IEEE Trans. Autom. Contr.
, 14
(2
), pp. 141
–149
. 5.
Dorato
, P.
, 1969
, “On the Inverse of Linear Dynamical Systems
,” IEEE Trans. Syst. Sci. Cybernet.
, 5
(1
), pp. 43
–48
. 6.
Zou
, Q.
, and Devasia
, S.
, 1999
, “Preview-Based Stable-Inversion for Output Tracking of Linear Systems
,” ASME J. Dyn. Syst. Meas. Control
, 121
(4
), pp. 625
–630
. 7.
Nijmeijer
, H.
, 1986
, “Right-Invertibility for a Class of Nonlinear Control Systems: A Geometric Approach
,” Syst. Control Lett.
, 7
(2
), pp. 125
–132
. 8.
Marro
, G.
, Prattichizzo
, D.
, and Zattoni
, E.
, 2002
, “Convolution Profiles for Right Inversion of Multivariable Non-minimum Phase Discrete-Time Systems
,” Automatica
, 38
(10
), pp. 1695
–1703
. 9.
Hou
, M.
, and Patton
, R. J.
, 1998
, “Input Observability and Input Reconstruction
,” Automatica
, 34
(6
), pp. 789
–794
. 10.
Estrada
, M. B.
, Garcia
, M. F.
, Malabre
, M.
, and García
, J. C. M.
, 2007
, “Left Invertibility and Duality for Linear Systems
,” Linear Algebra Appl.
, 425
(2–3
), pp. 345
–373
.11.
Kadam
, S. D.
, Chavan
, R. A.
, Rajiv
, A.
, and Palanthandalam-Madapusi
, H. J.
, 2019
, “A Perspective on Using Input Reconstruction for Command Following
,” Circuits, Syst. Signal Process.
, 38
(12
), pp. 5920
–5930
. 12.
Kadam
, S. D.
, Rao
, A.
, Prusty
, B.
, and Palanthandalam-Madapusi
, H. J.
, 2020
, “Selective Tracking Using Linear Trackability Analysis and Inversion-Based Tracking Control
,” American Control Conference
, Denver, CO
, July 1–3
, IEEE, pp. 5346
–5351
.13.
Kadam
, S. D.
, and Palanthandalam-Madapusi
, H. J.
, 2022
, “A Note on Invertibility and Relative Degree of Mimo LTI Systems
,” IFAC J. Syst. Control
, 20
, p. 100193
. 14.
Palanthandalam-Madapusi
, H. J.
, and Bernstein
, D. S.
, 2009
, “A Subspace Algorithm for Simultaneous Identification and Input Reconstruction
,” Int. J. Adapt. Control Signal Process.
, 23
(12
), pp. 1053
–1069
.15.
Fadali
, M. S.
, and Visioli
, A.
, 2012
, Digital Control Engineering: Analysis and Design
, Academic Press
, Burlington, MA
, p. 301
.
