Nonlinear discrete-time systems with delayed control: a reduction

In this work, the notion of reduction is introduced for discrete-time nonlinear input-delayed systems. The retarded dynamics is reduced to a new system which is free of delays and equivalent (in terms of stabilizability) to the original one. Different stabilizing strategies are proposed over the reduced model. Connections with existing predictor-based methods are discussed. The methodology is also worked out over particular classes of time-delay systems as sampled-data dynamics affected by an entire input delay

Reduction of discrete-time two-channel delayed systems

In this letter, the reduction method is extended to time-delay systems affected by two mismatched input delays. To this end, the intrinsic feedback structure of the retarded dynamics is exploited to deduce a reduced dynamics which is free of delays. Moreover, among other possibilities, an Immersion and Invariance feedback over the reduced dynamics is designed for achieving stabilization of the original systems. A chained sampled-data dynamics is used to show the effectiveness of the proposed control strategy through simulations

A unified smith predictor approach for power system damping control design using remote signals

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An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems

A general framework is presented for analyzing the stability and performance of nonlinear and linear parameter varying (LPV) time delayed systems. First, the input/output behavior of the time delay operator is bounded in the frequency domain by integral quadratic constraints (IQCs). A constant delay is a linear, time-invariant system and this leads to a simple, intuitive interpretation for these frequency domain constraints. This simple interpretation is used to derive new IQCs for both constant and varying delays. Second, the performance of nonlinear and LPV delayed systems is bounded using dissipation inequalities that incorporate IQCs. This step makes use of recent results that show, under mild technical conditions, that an IQC has an equivalent representation as a finite-horizon time-domain constraint. Numerical examples are provided to demonstrate the effectiveness of the method for both class of systems

Robust controller design for input-delayed systems using predictive feedback and an uncertainty estimator

[EN] This paper deals with the problem of stabilizing a class of input-delayed systems with (possibly) nonlinear uncertainties by using explicit delay compensation. It is well known that plain predictive schemes lack robustness with respect to uncertain model parameters. In this work, an uncertainty estimator is derived for input-delay systems and combined with a modified state predictor, which uses current available information of the estimated uncertainties. Furthermore, based on Lyapunov-Krasovskii functionals, a computable criterion to check robust stability of the closed-loop is developed and cast into a minimization problem constrained to an LMI. Additionally, for a given input delay, an iterative-LMI algorithm is proposed to design stabilizing tuning parameters. The main results are illustrated and validated using a numerical example with a second-order dynamic system.This work was partially supported by projects PROMETEOII/2013/004, Conselleria d Educació, Generalitat Valenciana, and TIN2014-56158-C4-4-P-AR, Ministerio de Economía y Competitividad, Spain.Sanz Diaz, R.; García Gil, PJ.; Albertos Pérez, P.; Zhong, Q. (2017). Robust controller design for input-delayed systems using predictive feedback and an uncertainty estimator. International Journal of Robust and Nonlinear Control. 27(10):1826-1840. https://doi.org/10.1002/rnc.3639S182618402710Stability and Stabilization of Systems with Time Delay. (2011). IEEE Control Systems, 31(1), 38-65. doi:10.1109/mcs.2010.939135Normey-Rico, J. E., Bordons, C., & Camacho, E. F. (1997). Improving the robustness of dead-time compensating PI controllers. Control Engineering Practice, 5(6), 801-810. doi:10.1016/s0967-0661(97)00064-6Michiels, W., & Niculescu, S.-I. (2003). 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Minimal data rate stabilization of nonlinear systems over networks with large delays

Control systems over networks with a finite data rate can be conveniently modeled as hybrid (impulsive) systems. For the class of nonlinear systems in feedfoward form, we design a hybrid controller which guarantees stability, in spite of the measurement noise due to the quantization, and of an arbitrarily large delay which affects the communication channel. The rate at which feedback packets are transmitted from the sensors to the actuators is shown to be arbitrarily close to the infimal one.Comment: 16 pages; references have now been adde