Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed methodPeer ReviewedPostprint (author's final draft

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

Parameter-Dependent Lyapunov Functions for Linear Systems With Constant Uncertainties

Robust stability of linear time-invariant systems with respect to structured uncertainties is considered. The small gain condition is sufficient to prove robust stability and scalings are typically used to reduce the conservatism of this condition. It is known that if the small gain condition is satisfied with constant scalings then there is a single quadratic Lyapunov function which proves robust stability with respect to all allowable time-varying perturbations. In this technical note we show that if the small gain condition is satisfied with frequency-varying scalings then an explicit parameter dependent Lyapunov function can be constructed to prove robust stability with respect to constant uncertainties. This Lyapunov function has a rational quadratic dependence on the uncertainties

On design of robust fault detection filter in finite-frequency domain with regional pole assignment

This brief is concerned with the fault detection (FD) filter design problem for an uncertain linear discrete-time system in the finite-frequency domain with regional pole assignment. An optimized FD filter is designed such that: 1) the FD dynamics is quadratically D-stable; 2) the effect from the exogenous disturbance on the residual is attenuated with respect to a minimized H∞-norm; and 3) the sensitivity of the residual to the fault is enhanced by means of a maximized H--norm. With the aid of the generalized Kalman-Yakubovich-Popov lemma, the mixed H--/H∞ performance and the D-stability requirement are guaranteed by solving a convex optimization problem. An iterative algorithm for designing the desired FD filter is proposed by evaluating the threshold on the generated residual function. A simulation result is exploited to illustrate the effectiveness of the proposed design technique.This work was supported in part by the Deanship of Scientific Research (DSR) at King Abdulaziz University in Saudi Arabia under Grant 16-135- 35-HiCi, the National Natural Science Foundation of China under Grants 61134009 and 61203139, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Robust gradient-based discrete-time iterative learning control algorithms

This paper considers the use of matrix models and the robustness of a gradient-based Iterative Learning Control (ILC) algorithm using both fixed learning gains and gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of matrix models in ILC. Matrix models make analysis clearer and provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non-causal controller dynamics. The results are compared with recent results for robust inverse-model based ILC algorithms and it is seen that the algorithm has the potential to improve robustness to high frequency modelling errors provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation