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Robust filtering for uncertain linear systems with delayed states and outputs
Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.Deals with the robust filtering problem for uncertain linear systems with delayed states and outputs. Both time-invariant and time-varying cases are considered. For the time-invariant case, an algebraic Riccati matrix inequality approach is proposed to design a robust H∞ filter such that the filtering process remains asymptotically stable for all admissible uncertainties, and the transfer function from the disturbance inputs to error state outputs satisfies the prespecified H∞ norm upper bound constraint. We establish the conditions under which the desired robust H ∞ filters exist, and derive the explicit expression of these filters. For the time-varying case, we develop a differential Riccati inequality method to design the robust filters. A numerical example is provided to demonstrate the validity of the proposed design approac
Bounds for Input- and State-to-Output Properties of Uncertain Linear Systems
We consider the effect of parametric uncertainty on properties of Linear Time
Invariant systems. Traditional approaches to this problem determine the
worst-case gains of the system over the uncertainty set. Whilst such approaches
are computationally tractable, the upper bound obtained is not necessarily
informative in terms of assessing the influence of the parameters on the system
performance. We present theoretical results that lead to simple, convex
algorithms producing parametric bounds on the -induced
input-to-output and state-to-output gains as a function of the uncertain
parameters. These bounds provide quantitative information about how the
uncertainty affects the system.Comment: To appear in the proceedings of the 8th IFAC Symposium on Robust
Control Design - ROCOND'1
MIMO First and Second Order Discrete Sliding Mode Controls of Uncertain Linear Systems under Implementation Imprecisions
The performance of a conventional model-based controller significantly
depends on the accuracy of the modeled dynamics. The model of a plant's
dynamics is subjected to errors in estimating the numerical values of the
physical parameters, and variations over operating environment conditions and
time. These errors and variations in the parameters of a model are the major
sources of uncertainty within the controller structure. Digital implementation
of controller software on an actual electronic control unit (ECU) introduces
another layer of uncertainty at the controller inputs/outputs. The
implementation uncertainties are mostly due to data sampling and quantization
via the analog-to-digital conversion (ADC) unit. The failure to address the
model and ADC uncertainties during the early stages of a controller design
cycle results in a costly and time consuming verification and validation (V&V)
process. In this paper, new formulations of the first and second order discrete
sliding mode controllers (DSMC) are presented for a general class of uncertain
linear systems. The knowledge of the ADC imprecisions is incorporated into the
proposed DSMCs via an online ADC uncertainty prediction mechanism to improve
the controller robustness characteristics. Moreover, the DSMCs are equipped
with adaptation laws to remove two different types of modeling uncertainties
(multiplicative and additive) from the parameters of the linear system model.
The proposed adaptive DSMCs are evaluated on a DC motor speed control problem
in real-time using a processor-in-the-loop (PIL) setup with an actual ECU. The
results show that the proposed SISO and MIMO second order DSMCs improve the
conventional SISO first order DSMC tracking performance by 69% and 84%,
respectively. Moreover, the proposed adaptation mechanism is able to remove the
uncertainties in the model by up to 90%.Comment: 10 pages, 11 figures, ASME 2017 Dynamic Systems and Control
Conferenc
Dilated LMI characterization for the robust finite time control of discrete-time uncertain linear systems
This paper provides new dilated linear matrix inequalities (LMIs) characterizations for the finite time boundedness (FTB) and the finite time stability (FTS) analysis of discrete-time uncertain linear systems. The dilated LMIs are later used to design a robust controller for the finite time control of discrete-time uncertain linear systems. The relevant feature of the proposed approach is the decoupling between the Lyapunov and the system matrices, that allows considering a parameter-dependent Lyapunov function. In this way, the conservativeness with respect to previous results is decreased. Numerical examples are used to illustrate the results.Peer ReviewedPostprint (author's final draft
Finite-time control for uncertain linear systems with disturbance inputs
We consider the static output feedback, finite-time disturbance rejection problem for linear systems with time-varying norm-bounded uncertainties. The first result provided in the paper is a sufficient condition for finite-time state feedback disturbance rejection in the presence of constant disturbances. This condition requires the solution of an LMI. Then we consider the more general output feedback case, which is shown to be reducible to the solution of an optimization problem involving bilinear matrix inequalities. Finally we deal with the case in which the disturbance is time-varying and generated by a linear system
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