Controller redesign to minimize uniform quantization errors in uncertain linear systems with fixed hardware constraints

We consider the classical emulation paradigm in which a controller is already designed for a linear time-invariant plant. Motivated by implementation constraints in real applications, we analyze the effects of ubiquitous low-cost quantizers on the closed-loop dynamics. Consequently, we address the robust control problem of an uncertain discrete-time linear process using a regulator affected by the effects of uniform quantization performed by the input–output converters and arithmetical unit. In this setup with fixed hardware resolutions, the regulator’s state-space realization is balanced to minimize the process’ state quantization error while simultaneously maintaining its desired transient response. To characterize the quantization error, we provide an ultimate bound for its worst-case scenario using the input-to-state stability framework. The minimization is performed using off-the-shelf tools, with a characterization of the resulting problem. Finally, a comparative numeric case study showing the tightness of the computed bound is discussed.