On the Output Controllability of Positive Discrete Linear Delay Systems

Mouhcine Naim,Fouad Lahmidi,Abdelwahed Namir,Mostafa Rachik

doi:10.1155/2017/3651271

Mouhcine Naim, Fouad Lahmidi + Show 2 more

Open Access

https://doi.org/10.1155/2017/3651271

Copy DOI

Abstract

Necessary and sufficient conditions for output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output are established. It is also shown that output reachability and null output controllability together imply output controllability.

Highlights

The research devoted to controllability was started by Kalman in the 1960s [1] and refers to linear dynamical systems
The following are examples of variations of controllability notions which have been introduced in the control literature: asymptotic controllability [5], relative controllability [6], constrained controllability [7], complete controllability [8], approximate controllability [9], small controllability [10], output controllability [11, 12], and so on
The control of a multilink cable-driven manipulator, where the task is typically defined in terms of end effector pose, rather than the joint positions and velocities which can define the system’s state [13], controlling the output of fixed-speed wind turbines in the electrical network, which can directly affect the behavior of power systems [14]

Summary

Introduction

The research devoted to controllability was started by Kalman in the 1960s [1] and refers to linear dynamical systems. Positive systems are a wide class of systems in which state variables and outputs are constrained to be positive, or at least nonnegative for all time whenever the initial conditions and inputs are nonnegative. The output reachability of positive discrete linear systems with state delay has been studied in [29]. In this paper we examine the issue of output reachability, null output controllability, and output controllability for positive linear systems with multiple delays in state, input, and output. These concepts are equivalent for unconstrained systems. We investigate the output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output, respectively, in Sections 3 and 4.

Preliminaries

Output Reachability

Null Output Controllability

Output Controllability

Numerical Examples

Conclusion