Observer-based state-feedback control design for LPV periodic discrete-time systems

This paper proposes new linear matrix inequality conditions to the observer-based control design problem for Linear Parameter Varying (LPV) periodic discrete-time systems. The time-varying parameters are considered to be available online (measured or estimated). In this way, periodic gain scheduling observers and controllers can be designed. Less conservative results in terms of the H∞ performance can be obtained if the variation rates of the parameters are known, otherwise arbitrarily fast variation can be considered. The H∞ guaranteed cost from the disturbance input to the error signal has been used for the observer design, and the state feedback control design considers the minimization of the H∞ bound from both error signal and input noise to the output of the controlled system. In this way, the designed controller provides robustness against inaccurate estimation. The analysis of the augmented system composed by the observer and controller is performed and numerical experiments illustrate the efficacy of the proposed method.