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Singular perturbations and time-scale methods in control theory: Survey 1976-1983. (English) Zbl 0532.93002
Summary: Recent progress in the use of singular perturbation and two-time-scale methods of modeling and design for control systems is reviewed. Over 350 references are organized into major problem areas. Representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application. The survey is aimed at engineers and applied mathematicians interested in model-order reduction, separation of time scales and allied simplified methods of control system analysis and design. The exposition does not assume prior knowledge of singular perturbation methods.

MSC:
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
34E15 Singular perturbations for ordinary differential equations
93A15 Large-scale systems
34D15 Singular perturbations of ordinary differential equations
93E20 Optimal stochastic control
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C10 Nonlinear systems in control theory
93B35 Sensitivity (robustness)
93E11 Filtering in stochastic control theory
93C40 Adaptive control/observation systems
93C05 Linear systems in control theory
93B05 Controllability
93B07 Observability
68U20 Simulation (MSC2010)
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