$H_2/H_{\infty }$ Control for Networked Control Systems with Asynchronous Communication

Abstract

This chapter tackles the problem of designing suboptimal $H_{2}/H_{\infty }$ controllers for linear NCSs subject to time-varying delays and packet dropouts. The approach relies on the formulation of the problem in terms of the minimization of a single scalar parameter that can be cast as an standard LMI problem, yielding a suboptimal cost-guaranteed solution. The formulation allows to trade-off performance and disturbance rejection, as the $H_2$ part of the control accounts for the optimization of a quadratic performance index, with an $L_2$-gain disturbance rejection constraint in the $H_{\infty }$ component. To characterize the network, only the lower and upper bounds for the delay interval, as well as the maximum number of consecutive dropouts are required. As a difference from previous works, the solution provided is independent of initial conditions.