By Dullerud G.E., Paganini F.

ISBN-10: 0387989471

ISBN-13: 9780387989471

Throughout the 90s powerful keep an eye on idea has obvious significant advances and completed a brand new adulthood, established round the inspiration of convexity. The target of this booklet is to provide a graduate-level direction in this conception that emphasizes those new advancements, yet whilst conveys the most rules and ubiquitous instruments on the center of the topic. Its pedagogical targets are to introduce a coherent and unified framework for learning the idea, to supply scholars with the control-theoretic heritage required to learn and give a contribution to the learn literature, and to give the most rules and demonstrations of the most important effects. The e-book should be of worth to mathematical researchers and laptop scientists, graduate scholars planning on doing study within the zone, and engineering practitioners requiring complex keep watch over strategies.

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**Additional info for A Course in Robust Control Theory - A Convex Approach**

**Example text**

In particular, the set of positive de nite matrices is a convex cone in H n , as de ned in the previous section. At this point we may well ask, how can we check whether a matrix is positive de nite? 9: If Q 2 H n then Q > 0 if and only if the eigenvalues of Q are all positive. Notice in particular that a positive de nite matrix is always invertible, and its inverse is also positive de nite. Also a matrix is positive semi-de nite exactly when none of its eigenvalues are negative in that case the number of strictly positive eigenvalues is equal to the rank of the matrix.

Linear Matrix Inequalities 49 to the following discussion, and furthermore in the exercises we will see that the Hermitian form can always be converted to the symmetric form. An important property of LMIs is that a list of them can always be converted to one LMI. To see this suppose we have the two LMIs F0 (X0 ) < Q0 and F1 (X1 ) < Q1 in the variables X0 and X1 in vector spaces X0 and X1 respectively. Then this is equivalent to the single LMI F (X ) < Q where X = (X0 X1 ) 2 X0 X1 and Q = Q00 Q0 1 and we de ne the function F : X0 X1 !

Here we have formulated LMIs in terms of the Hermitian matrices, which is the most general situation for our later analysis. In some problems LMIs are written over the space of symmetric matrices Sn, and this is the usual form employed for computation. 4. Linear Matrix Inequalities 49 to the following discussion, and furthermore in the exercises we will see that the Hermitian form can always be converted to the symmetric form. An important property of LMIs is that a list of them can always be converted to one LMI.

### A Course in Robust Control Theory - A Convex Approach by Dullerud G.E., Paganini F.

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