**Reference:**

S. Kanev,
B. De Schutter, and
M. Verhaegen,
"An ellipsoid algorithm for probabilistic robust controller design,"
*Systems & Control Letters*, vol. 49, no. 5, pp. 365-375,
Aug. 2003.

**Abstract:**

In this paper a new iterative approach to probabilistic robust
controller design is presented, which is applicable to any robust
controller/filter design problem that can be represented as an LMI
feasibility problem. Recently, a probabilistic Subgradient Iteration
algorithm was proposed for solving LMIs. It transforms the initial
feasibility problem to an equivalent convex optimization problem,
which is subsequently solved by means of an iterative algorithm. While
this algorithm always converges to a feasible solution in a finite
number of iterations, it requires that the radius of a non-empty ball
contained into the solution set is known *a-priori*. This
rather restrictive assumption is released in this paper, while
retaining the convergence property. Given an initial ellipsoid that
contains the solution set, the approach proposed here iteratively
generates a sequence of ellipsoids with decreasing volumes, all
containing the solution set. At each iteration a random uncertainty
sample is generated with a specified probability density, which
parametrizes an LMI. For this LMI the next minimum-volume ellipsoid
that contains the solution set is computed. An upper bound on the
maximum number of possible correction steps, that can be performed by
the algorithm before finding a feasible solution, is derived. A method
for finding an initial ellipsoid containing the solution set, which is
necessary for initialization of the optimization, is also given. The
proposed approach is illustrated on a real-life diesel actuator
benchmark model with real parametric uncertainty, for which a
*H*_{2} robust state-feedback controller is designed.

Online version of the paper

Corresponding technical report: pdf file (393 KB)

@article{KanDeS:02-017,

author={S. Kanev and B. {D}e Schutter and M. Verhaegen},

title={An ellipsoid algorithm for probabilistic robust controller design},

journal={Systems \& Control Letters},

volume={49},

number={5},

pages={365--375},

month=aug,

year={2003},

doi={10.1016/S0167-6911(03)00115-4}

}

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