
doi: 10.1137/0321020
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.
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
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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