H ∞ performance realisation and switching controller design for linear time‐invariant plant

This study focuses on the design of a switching controller, which includes several linear time‐invariant (LTI) controllers designed beforehand and independently, for a specific LTI plant. All of these LTI controllers are capable of stabilising the plant with corresponding H ∞ control performance criterions. It is shown that there exist suitable state space realisations of these controller transfer matrices that guarantee not only certain H ∞ control performance of the overall closed‐loop system under arbitrary switching but also corresponding H ∞ performances of local closed‐loop systems at switching points.