Sampling zero stability in sampled data control systems with delays using backward triangle sample and hold

The impact of time delays on the stability of sampling zeros in sampled-data (SD) control systems is investigated. While delays, arising from communication and computational latencies, are known to critically influence zero-dynamics stability, their specific effect on sampling zeros remains less explored. This work establishes novel conditions for sampling zero stability under time delays, employing the Backward Triangle Sample-and-Hold (BTSH) method for signal reconstruction. In particular, we analyze the asymptotic behavior of sampling zeros with respect to the system's relative degree and delay magnitude using BTSH. Moreover, through this analysis, we derive explicit stability conditions for these zeros, crucial for overall system performance. Finally, we provide a comparative analysis contrasting the stability properties under BTSH with those under the conventional Zero-Order Hold (ZOH) method in delayed settings. The theoretical findings are validated through a detailed numerical example, demonstrating the distinct advantages of BTSH in managing delay-induced zero-dynamics challenges.