ℋ ∞ Control for Two-Dimensional Markovian Jump Systems with State-Delays and Defective Mode Information

Abstract EN

This paper investigates the problem of ℋ∞ state-feedback control for a class of two-dimensional(2D) discrete-time Markovian jump linear time-delay systems with defective mode information.

The mathematical model of the 2D system is established based on the well-known Fornasini-Marchesini local state-space model, and the defective mode information simultaneously consistsof the exactly known, partially unknown, and uncertain transition probabilities.

By carefully analyzingthe features of the transition probability matrices, together with the convexification ofuncertain domains, a new ℋ∞ performance analysis criterion for the underlying system is firstlyderived, and then the ℋ∞ state-feedback controller synthesis is developed via a linearisation technique.

It is shown that the controller gains can be constructed by solving a set of linear matrixinequalities.

Finally, an illustrative example is provided to verify the effectiveness of the proposeddesign method.