Nonlinear Stabilization under Sampled and Delayed Measurements, and with Inputs Subject to Delay and Zero-Order Hold

TL;DR

This paper develops global asymptotic stabilization methods for nonlinear systems with long input and output delays, sampling, and zero-order hold, using predictor-based delay compensation and nominal feedback laws.

Contribution

It introduces two general results providing global stabilization for systems with arbitrary delays and sampling, extending previous open problems in networked control.

Findings

Achieves global asymptotic stability under long delays and sampling periods

Employs predictor-based delay compensation with nominal feedback laws

Provides solutions for nonlinear systems with sampled measurements and zero-order hold

Abstract

Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under the assumption that the system is stabilizable under sampled-data feedback for some sampling period, and then construct sampled-data feedback laws that achieve global asymptotic stabilization under arbitrarily long input and measurement delays. All the results employ "nominal" feedback laws designed for the continuous-time systems in the absence of delays, combined with "predictor-based" compensation of delays and the effect of sampling.