## Nonlinear robust hierarchical control for nonlinear uncertain systems.(English)Zbl 0958.93084

The paper studies a nonlinear robust control system with a set of moving nominal system equilibria, i.e., the equilibrium points which exist under admissible constant controls. The authors generalize the Barbashin-Krasovskij-LaSalle results on a Lyapunov function to the case where it is noncontinuous and lower semicontinuous. A theorem for global asymptotic robust stability of a compact positively invariant set is given. A hierarchical robust switching control strategy is constructed to stabilize a given nonlinear system. The goal of the strategy is a stabilization of subsystems generated by the parameterized equilibria. The hierarchical robust strategy is applied to a jet engine propulsion control problem with uncertain compressor pressure-flow maps.

### MSC:

 93D21 Adaptive or robust stabilization 93C10 Nonlinear systems in control theory 93A13 Hierarchical systems 93B12 Variable structure systems
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