New robust LMI synthesis conditions for mixed H2/H∞ gain-scheduled reduced-order DOF control of discrete-time LPV systems

Abstract

This paper investigates the problems of stabilization and mixed H2/H∞ reduced‐order dynamic output‐feedback control of discrete‐time linear systems. The synthesis conditions are formulated in terms of parameterdependent linear matrix inequalities (LMIs) combined with scalar parameters, dealing with state‐space models where the matrices depend polynomially on time‐varying parameters and are affected by norm‐bounded uncertainties. The motivation to handle these models comes from the context of networked control systems, particularly when a continuous‐time plant is controlled by a digitally implemented controller. The main technical contribution is a distinct LMI‐based condition for the dynamic output‐feedback problem, allowing an arbitrary structure (polynomial of arbitrary degree) for the measured output matrix. Additionally, an innovative heuristic is proposed to reduce the conservativeness of the stabilization problem. Numerical examples are provided to illustrate the potentialities of the approach to cope with several classes of discrete‐time linear systems (time‐invariant and time‐varying) and the efficiency of the proposed design conditions when compared with other methods available in the literature