Robust Local Stability Research Articles

Polyhedral Regions of Robust Local Stability for Linear Systems With Saturating Controls

The estimation of regions of robust local asymptotic stability of uncertain discrete-time linear systems with saturating control inputs is performed constructing robustly contractive polyhedral sets. New necessary and sufficient conditions for compact polyhedral sets be robustly contractive are derived. Based on linear programming formulation of these conditions, an effective non nomothetic expansion procedure is proposed for construction of robustly contractive potyhedral sets and consequent estimation of regions of robust local asymptotic stability of closed-loop saturated systems. The procedure starts with the supremal robustly contractive potyhedral set contained in the region of linear control arid progressively expands it over the region of nonlinear saturated control.

Robust local stability of multilayer recurrent neural networks

In this paper we derive a condition for robust local stability of multilayer recurrent neural networks with two hidden layers. The stability condition follows from linking theory about linearization, robustness analysis of linear systems under nonlinear perturbation and matrix inequalities. A characterization of the basin of attraction of the origin is given in terms of the level set of a quadratic Lyapunov function. In a similar way like for NL theory, local stability is imposed around the origin and the apparent basin of attraction is made large by applying the criterion, while the proven basin of attraction is relatively small due to conservatism of the criterion. Modifying dynamic backpropagation by the new stability condition is discussed and illustrated by simulation examples.

Local robust stability of mrac under persistent excitation assumption

AbstractIn this paper the local robust stability of model reference adaptive control for time‐varying plants with unmodelled dynamics under the persistent excitation condition is studied. It is shown that for arbitrary initial conditions of the adaptive system all signals in the adaptive loop are bounded if the command input is persistently exciting and the plant parameter variation and the magnitude of the unmodelled component are sufficiently small in the mean.