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

Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming

The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically designed after the features of the input signal. We suggest that in many applications, and notably those involving D/D and D/A conversion or actuation, the NTF should instead be shaped after the properties of the output/reconstruction filter. To this aim, we propose a framework for optimal design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite programming. Some examples illustrate how in practical cases the proposed strategy can outperform more standard approaches.Comment: 14 pages, 18 figures, journal. Code accompanying the paper is available at http://pydsm.googlecode.co

Robust Fixed-Order Controller Design with Common Lyapunov Strictly Positive Realness Characterization

This paper investigates the design of a robust fixed-order controller for a polytopic system with interval uncertainties, with the aim that the closed-loop stability is appropriately ensured and the performance specifications on sensitivity shaping are conformed in a specific finite frequency range. Utilizing the notion of common Lyapunov strictly positive realness (CL-SPRness), the equivalence between strictly positive realness (SPRness) and strictly bounded realness (SBRness) is elegantly established; and then the specifications on robust stability and performance are transformed into the SPRness of newly constructed systems and further characterized in the framework of linear matrix inequality (LMI) conditions. Compared with the traditional robust controller synthesis approaches, the proposed methodology here avoids the tedious yet mandatory evaluations of the specifications on all vertices of the polytopic system; only a one-time checking of matrix existence is needed exclusively, and thus the typically heavy computational burden involved (in such robust controller design problems) is considerably alleviated. Moreover, it is noteworthy that the proposed methodology additionally provides essential necessary and sufficient conditions for this robust controller design with the consideration of a prescribed finite frequency range; and therefore significantly less conservatism is attained in the system performance.Comment: 10 pages, 6 figure

Fixed-Order Controller Design for Systems with Polytopic Uncertainty Using LMIs

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex inner-approximation of the whole non- convex set of stabilizing controllers and depends on the choice of a central polynomial. It is shown that with an appropriate choice of the central polynomial, the set of all fixed-order controllers that place the closed-loop poles of a polytopic system in a disk centered on the real axis, can be outbounded with an LMI. This way, robust regional pole placement can be achieved by convex optimization for systems with polytopic uncertainty

Region of attraction analysis with Integral Quadratic Constraints

A general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Contro

An improved stability criterion for a class of Lur'e systems

Copyright © 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We consider the stability of the feedback connection of a linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program. By generalizing the class of candidate Lyapunov functions we improve on existing results in the literature. A Lyapunov function is constructed via the S-procedure from quadratic constraints established using the Karush-Kuhn-Tucker (KKT) conditions. The stability criterion can be expressed as a linear matrix inequality (LMI) condition. We discuss some simple examples that demonstrate the improved results

Frequency-domain stability conditions for split-path nonlinear systems

This paper considers the class of control systems containing so-called split-path nonlinear (SPAN) filters, which are designed to overcome some of the well-known fundamental limitations in linear time-invariant (LTI) control. In this work, we are interested in developing tools for the stability analysis of such systems using frequency-domain techniques. Hereto, we explicitly show the equivalence between a set of linear matrix inequalities (LMIs) with S-procedure terms, guaranteeing stability of the closed-loop (SPAN) system, and a frequency-domain condition. We also provide a systematic procedure for verifying the frequency-domain condition in a graphical manner. The results are illustrated through a nummerical case study.</p