Abstract
Abstract We introduce the concept of $\epsilon $-uncontrollability for random linear systems, i.e. linear systems in which the usual matrices have been replaced by random matrices. We also estimate the $\varepsilon $-uncontrollability in the case where the matrices come from the Gaussian orthogonal ensemble. Our proof utilizes tools from systems theory, probability theory and convex geometry.
Highlights
Controllability is one of the most fundamental concepts in systems theory and control theory
Dx = Ax + bu, y = Cx + du, dt where x = x(t) = (x1(t), x2(t), . . . , xn(t))t ∈ Rn is a vector describing the state of the system at time t, u = u(t) ∈ R is the input and y = y(t) is the m-vector of outputs
The situation is more complicated and we provide an upper bound for the -uncontrollability of a random system
Summary
Controllability is one of the most fundamental concepts in systems theory and control theory. In this case the definition of controllability goes as follows. In order to formulate a suitable concept of uncontrollability for random systems, we utilize a characterisation of the controllability of systems of the form (1.1). This is provided in the theorem (for more details see, for example, [4] Theorem 2.2).
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