مرکز منطقه ای اطلاع رساني علوم و فناوري - Comments on "Exact control of linear systems with multiple controls"

DocumentCode :

854258

Title :

Comments on "Exact control of linear systems with multiple controls"

Author :

Casiello, Francisco ; Loparo, Kenneth A.

Author_Institution :

E.N.A.C.E., Argentina

Volume :

Issue :

fYear :

1987

fDate :

11/1/1987 12:00:00 AM

Firstpage :

1020

Lastpage :

1021

Abstract :

Given a linear system $\\dot{x} = Ax + Bu$ , where $A$ and $B$ are $n \\times n$ and $n \\times m$ matrices, with $m \\leq n$ and $B$ is of full rank, Farlow\´s theorem in the paper gives a necessary condition for the existence of coefficients for $nm$ rectangular pulse functions that constitute the control vector, so that the state of the system is driven to zero in a finite given time. It is shown in this note that rank adj $(A - s_{i}I)$ , where $A$ has $n$ distinct eigenvalues $s_{i}, i = 1, 2,..., n$ , is one. As a result, there are only $n$ linearly independent equations in Farlow\´s condition for the $nm$ coefficients and as such only $n$ of the coefficients are determined uniquely. The other $n(m -1)$ coefficients can be chosen to achieve other desirable characteristics of the system response.