Abstract
Abstract Stability robustness in discrete-time multivariable feedback systems subject to noises and non-linear time-varying unmodelled dynamics is discussed. Based on the technique of functional analysis and the control algorithm advanced by Youla et al., we derive a necessary and sufficient condition for robust stabilization to tolerate the unmodelled dynamics and noises. The properties of the Schur function (Class S) is employed to synthesize the robust stabilizer. Furthermore, a necessary and sufficient condition for the solvability of such a robust stabilization problem is also presented by means of the Nevanlinna-Pick interpolation theory. In addition, neither the plant nor the controller has to be restricted to be stable or minimum-phase
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