Unstabilizability of Linear Unstable Systems with Input Limits

It is shown that a linear strictly unstable system with actuation limits can not be stabilized globally, regardless of whatever control methodology is applied. This has important implications for control practices, especially for the control of unstable plants whose dynamics may vary abruptly during operation. It also implies that a feedback controller should be stable by itself, which further aggravates the problem of controlling certain unstable plants in practice.