In this chapter, we consider again H ∞ optimal control, but we pursue a different approach. The starting point is a revised version of the bounded real lemma in which for a transfer matrix G the property || G || ∞ < 1 is characterized by a linear matrix inequality (LMI). Then the idea for solving the H ∞ optimal control problem is quite simple: Apply this characterization to the closed-loop transfer function F zw in order to get a description of suboptimal controllers. In doing so, the problem is that the characterization is not convex, but this property is needed to get necessary and sufficient optimality conditions. Some tricky algebra is required to get a convex characterization by three LMIs (Sect. 10.1).
KeywordsLinear Matrix Inequality Feedback System Step Response Optimal Controller Controller Synthesis
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Notes and References
- Chilali, M., Gahinet., P.: H ∞ design with pole placement constraints: an LMI approach, IEEE Trans. Autom. Control, pp. 358–367,1996.Google Scholar