PWL and PWA ℋ_∞ controller synthesis for uncertain PWA slab systems: LMI approach

Abstract

This article presents new piecewise-affine (PWA) and piecewise-linear (PWL) ℋ_∞ controller synthesis methods for uncertain PWA slab systems. The synthesis problems are formulated as convex programs subject to a set of Linear Matrix Inequalities (LMIs), which can then be solved efficiently using available software. No other synthesis methods available in the literature can design a PWA controller for an uncertain PWA system using convex optimisation without constraining the controller gain matrix. Therefore this is the main contribution of the article. The proposed controller synthesis methodologies are applied to a circuit example.

Keywords:

• ℋ_∞ control
• linear matrix inequalities
• piecewise-affine systems
• piecewise-linear systems

Acknowledgements

The authors would like to acknowledge NSERC and FQRNT for funding this research.