Sampled-Data Delayed Output Feedback Control of a Class of Nonlinear Systems

Co‐design of memorized controllers for global sampled‐data stabilization a class of nonlinear system with input delay

“…which means that system (11) can be globally stabilized by the the sampled-data controller (16). After using the coordinate transformation (3), it can be concluded that the nonlinear system (1) with input delay is globally asymptotically stable under the memorized sampled-data state feedback controller (10).…”

“…the augmented dynamic system (7) is globally asymptotically stable which means that the nominal part of system (4) is globally stabilized by the sampled-data controller (16). In other words, there always exists a Lyapunov function…”

“…For nonlinear system that is globally exponentially stabilized by global Lipschtiz controllers in the continuous-time domain [15], both fast sampling and small input-delay are required for preserving the global exponential stability under sampled-data controllers. Even for sampled-data output stabilization of low-triangular nonlinear system without time delay in [16], the potential of compensation between scaling gain and sampling period has not been fully explored to relax constraints on sampling period not to mention the constraints on time delay. As summarized in [10], input delay of arbitrary length can be compensated using continuous-time controllers while there is no such extension under sampled-data controllers.…”

Sampled‐data control of time‐delay uncertain systems with uncontrollable/unobservable linearization by memoryless feedback

“…Under certain linear growth conditions, it was proved that the GAS property is preservable when the input delay and sampling period are limited. 18,20,21 For globally Lipschitz time-delay systems, the work 10 showed that global exponential stability (GES) is achievable by globally Lipschitz state feedback under a fast sampling. In References 9 and 22, GAS by sampled-data output feedback was solved for a class of nonminimum-phase nonlinear systems under certain restrictive growth condition.…”

“…Recently, it has been shown that without imposing restrictive conditions such as global Lipschitz or linear growth, semiglobal asymptotic stabilization rather than GAS is still possible by sampled-data state and output feedback, respectively, under uniform observability and global asymptotic local exponential stabilizability. 16,17,21 Following the recent development, 1,18,20,21 we study in this article the problem of how to control time-delay systems with inherent nonlinearity by memoryless sampled-data feedback. The main contribution is to prove that for a significant class of nonlinear systems with state and input delays, GAS is achievable by nonsmooth sampled-data feedback, provided that the input delay is limited and the sampling period is fast enough, and the state delays are allowed to be large but bounded.…”