Digital output feedback event-based stabilization of nonlinear systems with state delays

In this paper, the stabilization problem of nonlinear time-delay systems by means of digital dynamic output feedback event-triggered controllers is addressed. In particular, for the class of control-affine nonlinear systems with state delays, a methodology for the design of quantized sampled-data observer-based event-triggered (QSOE) stabilizers is provided. As a first step, the notion of Dynamic Output Steepest Descent Feedback (DOSDF), induced by a class of Lyapunov–Krasovskii functionals, is suitably revised in order to cope with the design of QSOE stabilizers. Then, the stabilization in the sample-and-hold sense theory is used as a tool to prove the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that: the digital implementation of DOSDFs, updated through a proposed event-based mechanism, ensures the semi-global practical stability property of the related closed-loop system with arbitrarily small final target ball of the origin. In the theory here developed, aperiodic sampling and the non-uniform quantization of the input/output channels are taken into account. Possible discontinuities in the functions describing the DOSDF at hand are also managed enlarging the possibilities to successfully designing QSOE stabilizers. Moreover, the proposed QSOE stabilizer is described by easily implementable difference equations avoiding the necessity to solve differential equations for the correct application of the controller at hand. Nonlinear delay-free systems are addressed as a special case. The proposed results are validated through practical examples concerning a Glucose-Insulin system and a Continuous Stirred Tank Reactor system.