Polytopic best-mean H ∞ performance analysis

In [1], a novel best-mean approach to robust analysis and control over uncertain-parameters boxes was presented. This paper extends the results of [1] to convex uncertainty polytopes of arbitrary shape and arbitrary number of vertices, without an underlying parameters model. The paper addresses robust, polytopic, probabilistic H∞ analysis of linear systems and focuses on the performance distribution over the uncertainty region (rather than just on the performance bound, as is customary in robust control). It is assumed that all system instances over the uncertainty polytope may occur with equal probability; this uniform distribution assumption is common in robust statistical analysis and is known to be conservative. The proposed approach considers different disturbance attenuation levels (DALs) at the vertices of the uncertainty polytope. It is shown that, under the latter assumption, the mean disturbance attenuation level (DAL) over the polytope is the algebraic average of the DALs at the polytope's vertices. Thus, the mean DAL over the polytope can be optimized by minimizing the sum of the DALs at the vertices. The standard deviation of the DAL over the uncertain parameters-box is also addressed, and a method to minimize this standard deviation (in order to enforce uniform performance over the polytope) is shown. The state-feedback design example utilizes a theorem presented in [1]. A Monte-Carlo analysis veri es the statistics of the resulting closed-loop `pointwise' H∞-norms over the uncertainty region. Key–Words: Robust H∞ analysis, probabilistic performance, polytopic uncertainty