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Continuous-Time Markov Jump Linear Systems pp 183–212Cite as

Design Techniques

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Abstract

In this chapter we present some design techniques, expressed as linear matrix inequalities optimization problems for continuous-time MJLS. The linear matrix inequalities paradigm offers a flexible and efficient framework to computational applications, for which many powerful numerical packages exist. The chapter begins with a study of the stability radii of MJLS, which includes an algorithm and a spectral approach for obtaining upper bounds in the real and complex cases, plus a connection between stability radii and uncertainties in the transition rate matrix of the Markov jump process. Next, we proceed to the design of robust controllers satisfying a suboptimal H 2 criterion, which includes a study of robust mixed H 2/H ∞ controllers. At the end of the chapter, a solution of linear matrix inequalities is presented for the stationary robust linear filtering problem.

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Authors and Affiliations

  1. Polytechnic School, Department of Telecommunications, University of São Paulo, Av. Prof. Luciano Gualberto, Trav. 3 158, São Paulo, 05508-900, São Paulo, Brazil

    Oswaldo L.V. Costa

  2. Department of Systems and Control, LNCC/MCT, Nat. Lab. for Scientific Computing, Av. Getúlio Vargas, Quitandinha 333, Petrópolis, 25651-070, Rio de Janeiro, Brazil

    Marcelo D. Fragoso

  3. Department of Systems and Control, LNCC/MCT, Nat. Lab. for Scientific Computing, Av. Getúlio Vargas, Quitandinha 333, Petrópolis, 25651-070, Rio de Janeiro, Brazil

    Marcos G. Todorov

Authors
  1. Oswaldo L.V. Costa
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  2. Marcelo D. Fragoso
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  3. Marcos G. Todorov
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Costa, O., Fragoso, M., Todorov, M. (2013). Design Techniques. In: Continuous-Time Markov Jump Linear Systems. Probability and Its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34100-7_9

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