More on the controllability of linear time-invariant systems

A. Ailon; G. Langholz

doi:10.1080/00207178608933657

More on the controllability of linear time-invariant systems

A. Ailon
, G. Langholz

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

This study shows that a controllable system ẋ = Ax + Bu, where x is an n-vector, can be driven from an arbitrary initial condition x(0) = x₀ to an arbitrary final condition x(t_f = x_f by a polynomial control function of degree M = 2r + 1, where r = n − rank (B), through a polynomial trajectory of degree M. A simple algorithm for finding u by solving a set of linear equations, the solution of which yields the polynomial coefficients, is given.

Original language	English
Pages (from-to)	1161-1176
Number of pages	16
Journal	International Journal of Control
Volume	44
Issue number	4
DOIs	https://doi.org/10.1080/00207178608933657
State	Published - 1 Jan 1986

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications

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10.1080/00207178608933657

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abstract = "This study shows that a controllable system ẋ = Ax + Bu, where x is an n-vector, can be driven from an arbitrary initial condition x(0) = x0 to an arbitrary final condition x(tf = xf by a polynomial control function of degree M = 2r + 1, where r = n − rank (B), through a polynomial trajectory of degree M. A simple algorithm for finding u by solving a set of linear equations, the solution of which yields the polynomial coefficients, is given.",

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AB - This study shows that a controllable system ẋ = Ax + Bu, where x is an n-vector, can be driven from an arbitrary initial condition x(0) = x0 to an arbitrary final condition x(tf = xf by a polynomial control function of degree M = 2r + 1, where r = n − rank (B), through a polynomial trajectory of degree M. A simple algorithm for finding u by solving a set of linear equations, the solution of which yields the polynomial coefficients, is given.

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More on the controllability of linear time-invariant systems

Abstract

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