Output feedback guaranteeing cost control by matrix inequalities for discrete-time delay systems

This paper investigates the construction of guaranteeing cost dynamic output feedback controller for linear discrete-time delay systems with time-varying parameter uncertainties and with exogenous disturbances. A necessary and sufficient condition for a controller to have the guaranteeing cost property is given by a nonlinear matrix inequality. As a sufficient condition, a linear matrix inequality is derived, the solution of which can be used for constructing a control of the desired type. It is also shown that the resulted trajectory is input-to-state stable. A numerical example illustrates the application of the results.

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