Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions

Elimhan N. Mahmudov

doi:10.3934/naco.2021010

Article Contents

2022, Volume 12, Issue 2: 353-371. Doi: 10.3934/naco.2021010

This issue Previous Article Controllability and observability of stochastic implicit systems and stochastic GE-evolution operator Next Article A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem

Second order discrete time-varying and time-invariant linear continuous systems and Kalman type conditions

Elimhan N. Mahmudov^1,2,

1.
Department of Engineering Mathematics, Istanbul Technical University, Istanbul, Turkey
2.
Azerbaijan National Academy of Sciences Institute of Control Systems, Baku, Azerbaijan

Received: October 31, 2020

Revised: January 31, 2021

Published: June 2022

This paper is dedicated to the memory of Professor Lotfi A. Zadeh (1921-2017), Founder of Fuzzy logic and Fuzzy Mathematics

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Abstract

The paper deals with the controllability and observability of second order discrete linear time varying and linear time-invariant continuous systems in matrix form. To this case, we generalize the classical conditions for linear systems of the first order, without reducing them to systems of the first order. Within the framework of Kalman-type criteria, we investigate these concepts for second-order linear systems with discrete / continuous time; we define the initial values and input functions uniquely if and only if the observability and controllability matrices have full rank, respectively. Also a conceptual partner of controllability, that is, reachability of second order discrete time-varying systems is formulated and a necessary and sufficient condition for complete reachability is derived. Also the transfer function of the second order continuous-time linear state-space system is constructed. We have given numerical examples to illustrate the feasibility and effectiveness of the theoretical results obtained.

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Mathematics Subject Classification: Primary: 11D04, 39A70; Secondary: 93B05, 93B07.

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