Saturated Control of Linear Systems by Abdellah Benzaouia Fouad Mesquine & Mohamed Benhayoun

Author:Abdellah Benzaouia, Fouad Mesquine & Mohamed Benhayoun
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

and

The Algorithm 4.2 was run selecting matrix randomly, until an acceptable error is obtained in Step 7. The following values of matrices and were obtained:

Note that : That is, none of the eigenvalues of matrix is stable. To use the technique based on the solution of the algebraic equation of [2], the following matrix H, that satisfies all the required conditions of positive invariance and fulfilling the constraints on the control magnitude and rate, was selected: (4.13)–(4.14):

The fictitious constraints were also chosen to be large ( and ). Matrix K follows together with matrix by using (1.​42) and (4.23), respectively. Algorithm 4.2 was implemented using usual software, obtaining the following result:

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