Design of hybrid systems with guaranteed performance
- 11 November 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 1, 993-998 vol.1
- https://doi.org/10.1109/cdc.2000.912903
Abstract
We show that, for a linear system, any worst-case energy gain greater than the optimal H/sub /spl infin// norm is achievable by a logarithmically quantized state feedback. We also show how to derive the coarsest logarithmic quantizer provable via quadratic Lyapunov functions for a given level of performance. The smallest logarithmic base, for a given performance level, is obtained via a bisection algorithm applied to a parametric feasibility LMI problem. The result highlights the trade-off between performance degradation versus coarseness of quantization. Simulations suggest that the upper bound derived is a realistic measure of the actual performance under logarithmic quantization. The end result is the systematic design of a discrete event controller that stabilizes a linear system and guarantees a certain level of performance measured in terms of the worst-case close loop energy gain. The resulting hybrid system is implicitly verified.Keywords
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