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Deterministic and stochastic robustness measures for discrete systems. (English) Zbl 0661.93028
Given the linear discrete-time n-dimensional system $$x_{k+1}=Ax_ k$$ with constant stable $$n\times n$$-matrix A and constant matrices $$D_ 1,...,D_ m$$, for which (deterministic or random) numbers $$d_ 1,...,d_ m$$ the system remains stable, if A is replaced by $$A+\sum d_ kD_ k?$$ Upper bounds in terms of the spectral radius of A, and spectral properties of the $$D_ i's$$ are given (i) for the vector $$(d_ 1,...,d_ m)$$ is case of real $$d_ k$$, (ii) for the vector $$(v_ 1,...,v_ m)$$ of 2nd moments of $$d_ k$$, $$v_ k$$, in case of zero- mean, identically distributed uncorrelated random variables $$d_ k$$. Application: designing non-destabilizing feedback control.
Reviewer: V.Wihstutz

##### MSC:
 93B35 Sensitivity (robustness) 93E15 Stochastic stability in control theory 93C55 Discrete-time control/observation systems 93C05 Linear systems in control theory 93D15 Stabilization of systems by feedback
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