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Article
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SIAM Journal on Control and Optimization
Article . 1983 . Peer-reviewed
Data sources: Crossref
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Robust Stabilization of Uncertain Systems

Robust stabilization of uncertain systems
Authors: Willems, Jacques L.; Willems, Jan C.;

Robust Stabilization of Uncertain Systems

Abstract

In this paper we consider the systems described by \[dx = Axdt + Budt + \sum_i {\sigma _i F_i xd\beta _i } \qquad {\text{or}}\qquad \dot x = Ax + Bu + \sum_i {B_i F_i (x,t)C_i x,} \] and we will derive conditions under which there exists a feedback control law $u = Kx$ such that the closed loop system is stable for all $\sigma _i $ or (smooth) nonlinearities $F_i $. The nonlinearities $F_i $ and the noisy gains $\sigma _i d\beta _i $ are unknown uncertainties in the system, and the problem considered is to obtain a control law which is robust against these uncertainties, as far as stability is concerned.

Keywords

Invariant subspaces of linear operators, perfect robust stabilizability, Model systems in control theory, Stochastic ordinary differential equations (aspects of stochastic analysis), Discrete-time control/observation systems, time-invariant memoryless state feedback, Stabilization of systems by feedback, Nonlinear systems in control theory, Robustness and adaptive procedures (parametric inference), Stochastic stability in control theory, invariant subspaces

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Powered by OpenAIRE graph
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
62
Top 10%
Top 1%
Top 10%
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