Abstract
LMI methods find natural and fruitful application in robust control. The problem is to guarantee a desired closed-loop performance independently of the disturbance input, which is assumed bounded but unknown. In this case too it is possible to assign closed-loop eigenvalues in circular domains of the complex plane and to deal with pointwise norm constraints on input–output variables.
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Notes
- 1.
Notice there is no loss of generality in assuming P = I, so that ℰ(P) = ℰ(I), the unit-ball of ℝ n. Indeed, for any P > 0, there exists a unitary matrix M > 0 such that MPM′ = I, e.g., write P = TΛT′ with Λ positive-diagonal, take \(M=T\Lambda^{\frac{1}{2}}\). So Mℰ(P) = ℰ([MPM′]− 1) = ℰ(I) and in coordinates z = Mx (6.1) holds with W = ℰ(I) and A, w, Ω replaced by MAM′, Mw, MΩ.
Reference
Kouramas KI (2002) Control of linear systems with state and control constraints. Ph.D. Thesis, Imperial College, University of London
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Caravani, P. (2013). MIMO, x Observed, w ≠ 0 Unobserved, norm-Bounded. In: Modern Linear Control Design. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6943-8_6
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DOI: https://doi.org/10.1007/978-1-4614-6943-8_6
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