A Survey on Stability Analysis of Discrete-Time Piecewise Affine Systems
| Authors: | Biswas Pratik, Dept. of Electrical Engineering, Stanford University, United States
Grieder Pascal, Automatic Control Laboratory, ETH Zurich, Switzerland
Loefberg Johan, Automatic Control Laboratory, ETH Zurich, Switzerland
Morari Manfred, Automatic Control Laboratory, ETH Zurich, Switzerland |
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| Topic: | 1.3 Discrete Event and Hybrid Systems |
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| Session: | Hybrid Dynamic Systems |
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| Keywords: | Piecewise Affine Systems, Stability, Predictive Control,Sum-of-Squares |
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Abstract
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 withvarying degrees of conservativeness are available, for analyzingstability of PWA systems. This survey introduces the mostpromising existing methods and adapts them to discrete-time PWAsystems. Specifically, we investigate the computation of commonquadratic, common quartic, piecewise affine, piecewise quadraticand piecewise quartic Lyapunov functions using linear programming,semi-definite programming and sum-of-squares techniques.Subsequently, the different methods are compared regarding thelikelihood of finding a certificate of stability and computationrun time. To this end, an extensivecase study is performed.
