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MIMO, x Observed, w = 0

  • Paolo Caravani
Chapter

Abstract

Although assignment and stabilization problems discussed in the SISO case can be formulated and solved for MIMO systems, this extension requires discussion of deeper algebraic-geometric concepts making the controller design less direct: machine computation and coding is ultimately required. In most practical situations, on the other hand, assigning precise values to the closed-loop eigenvalues is not strictly necessary, being sufficient to prescribe their membership to certain subsets of the complex plane (for example, the unit circle in the discrete-time case). For this reason in the MIMO case we prefer to reformulate the problem with the use of modern optimization tools [2] that are computationally very efficient and allow to address design aspects like constraints on input and output variables that would be impossible to deal with by assignment-based methods.

Keywords

Lyapunov Function Asymptotic Stability Linear Matrix Inequality Common Lyapunov Function Positive Invariance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    Boyd S (2008) CVX downloadable from: http://www.stanford.edu/~boyd/cvx/
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    Boyd S, El Ghaoui L, Feron L et al (1994) LMI in systems and control theory. SIAM, Philadelphia. Downloadable from: http://www.stanford.edu/~boyd/lmibook.pdf
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    Chilali M, Gahinet P (1996) H design with pole placement constraints: an LMI approach. IEEE-TAC 41(3):358–367MathSciNetMATHGoogle Scholar
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    Golub GH, Van Loan CF (1983) Matrix computations. John Hopkins University Press, BaltimoreMATHGoogle Scholar
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    Wie B, Bernstein D (1992) Benchmark problem for robust control design. J Guid Contr 15:1057–1059CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Paolo Caravani
    • 1
  1. 1.Electrical and Information EngineeringDEWS - University of L’AquilaL’Aquila (AQ)Italy

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