scholarly journals Robust Admissibilization of Descriptor Systems by Static Output-Feedback: An LMI Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
M. Chaabane ◽  
F. Tadeo ◽  
D. Mehdi ◽  
M. Souissi
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Initial Value ◽  
Feedback Controllers ◽  
Classical State ◽  
Static Output

The problem of the stabilization of descriptor systems in continuous-time via static output-feedback is studied in this paper and an approach to solve it is proposed. For this, sufficient conditions are derived for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). These conditions are expressed in terms of a strict Linear Matrix Inequality (LMI); so they are tractable using numerical computations. The proposed controller design methodology is based on two steps: the first is dedicated to synthesizing a classical state-feedback controller, which is used as the initial value for the second step, which uses an LMI problem to obtain static output-feedback controllers that give admissibility. Finally, a numerical example is given to illustrate the results.

scholarly journals Design of Static Output Feedback Controller for Fractional-Order T-S Fuzzy System

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhile Xia
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Matrix Decomposition ◽  
Order Theory ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Feedback Controllers ◽  
Static Output

This paper studies the design of fuzzy static output feedback controllers for two kinds of fractional-order T-S fuzzy systems. The fractional order α satisfies 0<α<1 and 1≤α<2. Based on the fractional order theory, matrix decomposition technique, and projection theorem, four new sufficient conditions for the asymptotic stability of the system and the corresponding controller design methods are given. All the results can be expressed by linear matrix inequalities, and the relationship between fuzzy subsystems is also considered. These have great advantages in solving the results and reducing the conservatism. Finally, a simulation example is given to show the effectiveness of the proposed method.

THE CONTROLLER DESIGN FOR SINGULAR FRACTIONAL-ORDER SYSTEMS WITH FRACTIONAL ORDER 0 <α< 1

2018 ◽  
Vol 60 (2) ◽  
pp. 230-248
Author(s):  
T. ZHAN ◽  
S. P. MA
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Fractional Order Systems ◽  
Static Output

We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order $\unicode[STIX]{x1D6FC}$ when $0<\unicode[STIX]{x1D6FC}<1$. All the results are given by linear matrix inequalities. First, a new sufficient and necessary condition for the admissibility of singular fractional-order systems is presented. Then based on the admissible result, not only are sufficient conditions for designing pseudostate and static output feedback controllers obtained, but also sufficient and necessary conditions are presented by using different methods that guarantee the admissibility of the closed-loop systems. Finally, the effectiveness of the proposed approach is demonstrated by numerical simulations and a real-world example.

scholarly journals Static Output-Feedback Control for Vehicle Suspensions: A Single-Step Linear Matrix Inequality Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Josep Rubió-Massegú ◽  
Francisco Palacios-Quiñonero ◽  
Josep M. Rossell ◽  
Hamid Reza Karimi
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Vehicle Suspension ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequality ◽  
Feedback Controllers ◽  
Feedback Information ◽  
Static Output

In this paper, a new strategy to design static output-feedback controllers for a class of vehicle suspension systems is presented. A theoretical background on recent advances in output-feedback control is first provided, which makes possible an effective synthesis of static output-feedback controllers by solving a single linear matrix inequality optimization problem. Next, a simplified model of a quarter-car suspension system is proposed, taking the ride comfort, suspension stroke, road holding ability, and control effort as the main performance criteria in the vehicle suspension design. The new approach is then used to design a static output-feedbackH∞controller that only uses the suspension deflection and the sprung mass velocity as feedback information. Numerical simulations indicate that, despite the restricted feedback information, this static output-feedbackH∞controller exhibits an excellent behavior in terms of both frequency and time responses, when compared with the corresponding state-feedbackH∞controller.

scholarly journals PiecewiseH∞Static Output Feedback Controller Design for Nonlinear Systems Based on T-S Affine Fuzzy Models

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xingang Zhao
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Output Feedback Controller ◽  
Fuzzy Models ◽  
Complex Nonlinear Systems ◽  
Static Output

This paper is concerned with the problem of designingH∞controllers via static output feedback controller for a class of complex nonlinear systems, which is approximated by continuous-time affine fuzzy models. A decomposition method is presented to divide the output-space into different operating regions and interpolation regions. Based on this partition, a novel piecewise controller with affine terms via static output feedback is designed. By using a dilated linear matrix inequality (LMI) characterization, some nonconvex conditions are converted into convex ones to make the asymptotic stability andH∞performance of the closed-looped system. The effectiveness of the proposed method is illustrated by a numerical example.

scholarly journals Finite-Time H∞ Static Output Feedback Control for Itô Stochastic Markovian Jump Systems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1709
Author(s):  
Liu Xikui ◽  
Teng Yapeng ◽  
Li Yan
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Static Output Feedback ◽  
Transition Rates ◽  
Feedback Controllers ◽  
Static Output Feedback Control ◽  
Static Output

This paper focuses on the problem of finite-time H∞ static output feedback control for Ito^ stochastic systems with Markovian jumps (MJs). First of all, by introducing a new state vector and a novel signal, several sufficient conditions for the existence of static output feedback controllers are established for the considered systems with completely known transition rates (CKTRs) and partially known transition rates (PKTRs), respectively. Then the static output feedback controllers are designed via solving linear matrix inequalities (LMIs), which ensure the closed-loop systems are stochastic H∞ finite-time boundedness. The validity of the developed method was demonstrated through two examples.

scholarly journals Resilient asynchronous H∞ control designed for discrete-time Markov jump systems: Static output feedback case

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774770
Author(s):  
Xiao Lu ◽  
Lei Yang ◽  
Haixia Wang ◽  
Yuxia Li
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Traffic Control ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Markov Jump ◽  
Markov Jump Linear Systems ◽  
Static Output

This article is concerned with the problem of resilient asynchronous H∞ static output feedback control for discrete-time Markov jump linear systems. By Finsler’s Lemma, and with the help of two sets of slack variables, the product terms of system matrices and Lyapunov matrices are decoupled. Resilient asynchronous controller is designed to improve the robustness of the controller and overcome the drawback that the controller cannot get the information of the system’s mode. The controller that makes sure the closed-loop system is stochastically stable and with prescribed H∞ performance is designed. The bilinear matrix inequalities are given as the sufficient conditions for the controller design, which can be solved using linear matrix inequalities along with line search. This control strategy can be used in many practical application fields, such as robot control, aircraft, and traffic control.

Finite-Frequency Static Output Feedback H∞ Control of Continuous-Time T–S Fuzzy Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Redouane Chaibi ◽  
Ismail Er Rachid ◽  
El Houssaine Tissir ◽  
Abdelaziz Hmamed
Keyword(s):  
Output Feedback ◽  
Continuous Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Takagi Sugeno ◽  
Static Output

This paper is concerned with finite-frequency static output feedback (SOF) [Formula: see text] control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy systems. With the aid of the generalized Kalman–Yakubovich–Popov (GKYP) lemma, sufficient conditions for the existence of the finite-frequency SOF [Formula: see text] control are presented. The bilinear matrix inequalities are converted to a set of linear matrix inequalities, with the aid of some special derivations. Two practical examples are given to demonstrate the effectiveness of the proposed method.

Robust stabilization of a chemical reactor

2009 ◽  
Vol 63 (5) ◽  
Author(s):  
Monika Bakošová ◽  
Dalibor Puna ◽  
Petr Dostál ◽  
Jana Závacká
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Exothermic Reaction ◽  
Robust Stabilization ◽  
Output Feedback Control ◽  
Chemical Reactor ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Continuous Stirred Tank Reactor ◽  
Static Output

AbstractRobust static output feedback control was applied to a continuous stirred tank reactor with parametric uncertainty and multiple steady states in which exothermic reaction takes place. The problem of robust controller design was converted to a solution of linear matrix inequalities and a computationally simple non-iterative algorithm is presented. The possibility of using robust static output feedback for stabilization of reactors with uncertainty and comparison of robust P and PI controllers with an optimal controller is demonstrated by simulation results.

Multivariable Aeroengine PID Control With Amplitude Saturation: An LMI Solution

2010 ◽  
Author(s):  
Daoliang Tan ◽  
Ai He ◽  
Xi Wang ◽  
Yun Liu
Keyword(s):  
Gas Turbine ◽  
Output Feedback ◽  
Pid Controller ◽  
Controller Design ◽  
Gas Turbine Engine ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Engine Control ◽  
Turbine Engine ◽  
Static Output

This paper presents an approach to automatic tuning of the parameters of a PID controller for the multivariable gas turbine engine control, taking into account amplitude saturation and model nonstrict-properness. First of all, we illustrate that the PID controller design problem can be transformed into seeking a static output feedback controller for some augmented state-space model. Then we compute an initial stabilizable parameters of the involved PID controller in the strictly proper case, using a well-known static output feedback algorithm. As far as a non-strictly proper model is concerned, this paper uses a degenerate linear transformation to change its output equation into a strictly proper form. The drawback of the initially computed PID controller lies in its high gains (triggering amplitude saturation) that prevent it from being applicable to practical gas turbine engine control. In this paper, we build on a linear matrix inequality (LMI) based antiwindup scheme to address the constraints from amplitude saturation. Both of these problems are formulated in the LMI framework and can be efficiently solved using off-the-shelf software. Experimental results show the promising performance of the proposed method.

scholarly journals Static Output Feedback Control Design for Descriptor Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed Yagoubi
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Design Method ◽  
Output Feedback Control ◽  
Descriptor Systems ◽  
Static Output Feedback ◽  
Closed Loop System ◽  
Static Output Feedback Control ◽  
Descriptor Observer ◽  
Static Output

The static output feedback (SOF) synthesis problem for descriptor systems is considered in this paper. LMI-based algorithms are proposed to find potentially structured SOF gains ensuring admissibility and evenH∞performance of the closed-loop system. These algorithms are then used to propose a (descriptor) observer-basedH∞controller design method. An alternative technique for determining such separated estimation/control structure, after the design step, is also proposed. Several numerical examples, throughout the paper, demonstrate the effectiveness of the proposed algorithms.

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