Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

[EN] The problem of output stabilization and disturbance rejection for input-delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov-Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed-loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.PROMETEOII/2013/004; Conselleria d'Educacio; Generalitat Valenciana, Grant/Award Number: TIN2014-56158-C4-4-P-AR; Ministerio de Economia y Competitividad, Grant/Award Number: FPI-UPV 2014; Universitat Politecnica de ValenciaSanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2018). Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer. International Journal of Robust and Nonlinear Control. 28(6):2457-2467. https://doi.org/10.1002/rnc.4027S24572467286Stability and Stabilization of Systems with Time Delay. (2011). IEEE Control Systems, 31(1), 38-65. doi:10.1109/mcs.2010.939135Fridman, E. (2014). Introduction to Time-Delay Systems. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-09393-2Watanabe, K., & Ito, M. (1981). A process-model control for linear systems with delay. 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A fractional representation approach to the robust regulation problem for MIMO systems

The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parametrization of all robustly regulating controllers. The main results are formulated with minimal assumptions and without using coprime factorizations thus guaranteeing applicability with a very general class of systems. In addition to theoretical results, the design of robust controllers is addressed. The results are illustrated by two examples involving a delay and a heat equation.Comment: 23 pages, 3 figures, submitted to International Journal of Robust and Nonlinear Contro

Adaptive Backstepping Controller Design for Stochastic Jump Systems

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