1,315 research outputs found

    Fixed-order H-infinity controller design for systems with ellipsoidal parametric uncertainty

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    In this paper, fixed-order robust H-infinity controller design for systems with ellipsoidal parametric uncertainty based on parameter dependent Lyapunov functions is studied. Using the concept of Strictly Positive Realness (SPRness) of transfer functions, a fixed-order robust control design method in terms of solution to a set of Linear Matrix Inequalities (LMIs) is proposed. Since, controller parameters are decision variables, any controller structure, such as PID, can be considered. The weighted infinity-norm of closed loop sensitivity functions are considered as performance specification in the synthesis problem. The simulation results show the effectiveness of the proposed method

    Value-set-based approach to robust stability analysis for ellipsoidal families of fractional-order polynomials with complicated uncertainty structure

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    This paper presents the application of a value-set-based graphical approach to robust stability analysis for the ellipsoidal families of fractional-order polynomials with a complex structure of parametric uncertainty. More specifically, the article focuses on the families of fractional-order linear time-invariant polynomials with affine linear, multilinear, polynomic, and general uncertainty structure, combined with the uncertainty bounding set in the shape of an ellipsoid. The robust stability of these families is investigated using the zero exclusion condition, supported by the numerical computation and visualization of the value sets. Four illustrative examples are elaborated, including the comparison with the families of fractional-order polynomials having the standard box-shaped uncertainty bounding set, in order to demonstrate the applicability of this method. © 2019 by the authors.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)

    Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach

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    Simple Approximations of Semialgebraic Sets and their Applications to Control

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    Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance the solution set of linear matrix inequalities or the Schur/Hurwitz stability domains. These sets often have very complicated shapes (non-convex, and even non-connected), which renders very difficult their manipulation. It is therefore of considerable importance to find simple-enough approximations of these sets, able to capture their main characteristics while maintaining a low level of complexity. For these reasons, in the past years several convex approximations, based for instance on hyperrect-angles, polytopes, or ellipsoids have been proposed. In this work, we move a step further, and propose possibly non-convex approximations , based on a small volume polynomial superlevel set of a single positive polynomial of given degree. We show how these sets can be easily approximated by minimizing the L1 norm of the polynomial over the semialgebraic set, subject to positivity constraints. Intuitively, this corresponds to the trace minimization heuristic commonly encounter in minimum volume ellipsoid problems. From a computational viewpoint, we design a hierarchy of linear matrix inequality problems to generate these approximations, and we provide theoretically rigorous convergence results, in the sense that the hierarchy of outer approximations converges in volume (or, equivalently, almost everywhere and almost uniformly) to the original set. Two main applications of the proposed approach are considered. The first one aims at reconstruction/approximation of sets from a finite number of samples. In the second one, we show how the concept of polynomial superlevel set can be used to generate samples uniformly distributed on a given semialgebraic set. The efficiency of the proposed approach is demonstrated by different numerical examples

    Robust Stability of Time-varying Polytopic Systems by the Attractive Ellipsoid Method

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    This paper concerns the robust stabilization of continuous-time polytopic systems subject to unknown but bounded perturbations. To tackle this problem, the attractive ellipsoid method (AEM) is employed. The AEM aims to determine an asymptotically attractive (invariant) ellipsoid such that the state trajectories of the system converge to a small neighborhood of the origin despite the presence of nonvanishing perturbations. An alternative form of the elimination lemma is used to derive new LMI conditions, where the state-space matrices are decoupled from the stabilizing Lyapunov matrix. Then a robust state-feedback control law is obtained by semi-definite convex optimization, which is numerically tractable. Further, the gain-scheduled state-feedback control problem is considered within the AEM framework. Numerical examples are given to illustrate the proposed AEM and its improvements over previous works. Precisely, it is demonstrated that the minimal size ellipsoids obtained by the proposed AEM are smaller compared to previous works, and thus the proposed control design is less conservative
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