Abstract

In the present work, motivated by the continuous reduction in sensor costs and wireless communications, we consider the control of single-input two-outputs (SITO) linear time invariant (LTI) systems, either stable or unstable, over an additive white noise (AWN) channel located over the control path (between the controller and the plant model). We characterize the stability of the closed-loop by means of the channel Signal-to-Noise Ratio (SNR). We consider first the case of stable SITO models and propose a design for closed-loop stability that achieves the user desired channel SNR level. We then extend the result to include performance as tracking of constant setpoints. We consider second the case of unstable SITO models for which we find an infimal channel SNR level for stability. Below this value no stability is possible, above this value stability is achieved. We then extend the channel SNR result for unstable SITO plant models to include the same closed-loop performance, stated as stability and tracking of constant setpoints. In this case performance is achieved by designing a complementary sensitivity that satisfies the interpolation conditions needed to avoid the cancellation by the controller of any unstable poles in the plant model. We illustrate the obtained results with examples offering insight into the interplay of the different elements of these same results.