LMI-Based Optimization

  • Mohammad Fathi
  • Hassan Bevrani


In this chapter, following an introduction on the fundamentals of linear matrix inequalities (LMIs), the application of LMIs to solve convex optimization problems, using numerical examples, is explained. Then, the robust optimization problems are formulated and solved via the LMI-based H and mixed H2H optimization techniques. In order to solve non-convex optimization problems an iterative LMI is addressed. Finally, the effectiveness of given LMI-based optimization techniques in control synthesis is emphasized and several illustrative examples are given.


Linear matrix inequalities (LMI) Robust optimization Optimal H control Multi-objective optimization Performance index Non-convex optimization 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mohammad Fathi
    • 1
  • Hassan Bevrani
    • 1
  1. 1.University of KurdistanKurdistanIran

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