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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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