LMI conditions for the existence of polynomially parameter-dependent Lyapunov functions assuring robust stability

@article{Oliveira2005LMICF,
  title={LMI conditions for the existence of polynomially parameter-dependent Lyapunov functions assuring robust stability},
  author={R. C. L. F. Oliveira and P. L. D. Peres},
  journal={Proceedings of the 44th IEEE Conference on Decision and Control},
  year={2005},
  pages={1660-1665}
}
The robust stability of uncertain systems in polytopic domains is investigated by means of homogeneous polynomially parameter-dependent Lyapunov (HPPDL) functions which are quadratic with respect to the state variables. A systematic procedure to construct linear matrix inequality (LMI) conditions whose solutions assure the existence of HPPDL functions of increasing degree is given. For each degree, a sequence of relaxations based on real algebraic methods provides sufficient LMI conditions of… CONTINUE READING
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