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A Survey on Stability Analysis of Discrete-Time Piecewise Affine Systems


P. Biswas, P. Grieder, J. Löfberg, M. Morari

IFAC World Congress, Prague, Czech Republic

Piecewise affine (PWA) systems are useful models for describing non-linear and hybrid systems. They also result from LTI systems subject to constrained optimal control. A wide range of methods with varying degrees of conservativeness are available for analyzing stability of PWA systems. This survey introduces the most promising existing methods and adapts them to discrete-time PWA systems. Specifically, we investigate the computation of common quadratic, common quartic, piecewise affine, piecewise quadratic and piecewise quartic Lyapunov functions using linear programming, semi-definite programming and sum-of-squares techniques. Subsequently, the different methods are compared regarding the likelihood of finding a certificate of stability and computation run time. The objective is to provide the reader with a practical `recipe' for analyzing PWA systems. To this end, an extensive case study is performed.


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% Autogenerated BibTeX entry
@InProceedings { BisEtal:2005:IFA_2030,
    author={P. Biswas and P. Grieder and J. L{\"o}fberg and M. Morari},
    title={{A Survey on Stability Analysis of Discrete-Time Piecewise
	  Affine Systems}},
    booktitle={IFAC World Congress},
    address={Prague, Czech Republic},
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