Generalized PIO Design for Uncertain Discrete Time Systems

Considering the uncertain discrete time systems of Linear Parameter Varying (LPV) type, in this paper an approach for the synthesis of robust Proporcional+Integral Observers (PIO) is presented. From LPV systems characterized with polytopical uncertainties, the method of design is based on considering a dynamics extended of the typical PIO, in order to transform the design of the matrices of the dynamics of the observer, as a design of the gain of Static Output Feedback (SOF) of a problem of robust control. Under these conditions and from the norms H2/H∞ described as Linear Matrix Inequalities (LMI), the criteria to obtain the gain in the SOF problem are established; taking into account performance indices in H2 and H∞, under the presence of uncertainties and disturbances. In order to illustrate the results and the performance of the state robust estimation of states, some numerical examples are evaluated. Key–Words: Discrete-time systems. LPV Systems. Proportional+Integral Observers (PIO). Linear Matrix Inequalities (LMI).H2-H∞ Norms