Partial compensation for uncertain discrete systems
The author considers systems of the form \[ x(k+1)=[A+\Delta A(\sigma(k))]x(k)+Bu(k)+Ev(\sigma(k)) \] with known matrices \(A\), \(\Delta A\), \(B\), \(E\) and disturbance vector \(v\) of appropriate dimension and with appropriate properties such as stabilizability, continuity etc. The vector \(\sigma(.)\) of uncertainties takes values in a prescribed compact set. Then a nonlinear feedback control is proposed which is based on the solution to a certain Lyapunov equation. Conditions are formulated which guarantee that the resulting controlled system is practically stable. The results are illustrated by an example with two states and two control variables.
scientific article; zbMATH DE number 1501672