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A gradient flow approach to the robust pole‐placement problem
Author(s) -
Lam James,
Van WeiYong
Publication year - 1995
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4590050303
Subject(s) - differentiable function , mathematics , eigenvalues and eigenvectors , singularity , balanced flow , mathematical optimization , ode , minification , descent direction , gradient descent , computer science , mathematical analysis , artificial neural network , machine learning , physics , quantum mechanics
This paper provides a computational procedure for a type of robust pole‐placement problem. By exploiting the differentiability nature of the objective function based on the Frobenius norm condition number, the minimization problem is formulated in terms of a gradient flow to which standard ODE numerical routines can be applied. It is shown that a minimum point exists for the objective function. The algorithm is efficient and faces no singularity problem with the resulting eigenvector matrix. A numerical example is used to illustrate the technique and comparison with other methods is made.