scholarly journals Robust Switching Rule Design for Boost Converters with Uncertain Parameters and Disturbances

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Yang ◽  
Hamid Reza Karimi ◽  
Zhengrong Xiang
Keyword(s):  
Lyapunov Function ◽  
Linear System ◽  
Design Problem ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Common Lyapunov Function ◽  
Reference Tracking ◽  
Boost Converters ◽  
Switching Rule

This paper is concerned with the design problem of robust switching rule for Boost converters with uncertain parameters and disturbances. Firstly, the Boost converter is modeled as a switched affine linear system with uncertain parameters and disturbances. Then, using common Lyapunov function approach and linear matrix inequality (LMI) technique, a novel switching rule is proposed such that the model reference tracking performance is satisfied. Finally, a simulation result is provided to show the validity of the proposed method.

Control of a small helicopter with linear matrix inequality-based design assuring stability and performance

2019 ◽  
Vol 234 (3) ◽  
pp. 624-639
Author(s):  
İsmail Hakkı Şahin ◽  
Coşku Kasnakoğlu
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Parameter ◽  
Common Lyapunov Function ◽  
Affine Parameter ◽  
Dependent Model ◽  
And Performance ◽  
Parameter Dependent ◽  
Grid Based

This article focuses on linear matrix inequality-based controller designs that can achieve stabilization and reference tracking for a small unmanned helicopter at various flight conditions. A nonlinear mathematical model of a small-scale helicopter is constructed. Then trim conditions are found and linearized around different equilibrium points. Local [Formula: see text] controllers are designed at trim conditions based on the local linear models. The pointwise controllers achieve local stability and performance, but fail at stabilization and tracking over the full envelope. A scheduling controller is built by blending the local controller outputs. In addition, grid-based [Formula: see text] controllers are designed at each operating point with common Lyapunov function. This allows controller scheduling between the adjacent design points with guaranteed stability and performance across the design envelope. Based on the family of linear systems which are obtained from the nonlinear model, an affine parameter-dependent model is built to exploit the approximate linear parameter dependency. Then, a parameter-dependent linear parameter varying controller is synthesized for the affine parameter-dependent model. Although local performance is satisfactory for all given design methods, local [Formula: see text] controllers and affine parameter-dependent controller cannot yield satisfactory performance over the full flight envelope apart from the grid-based controller with common Lyapunov function approach.

scholarly journals Robust Observer Design for Switched Positive Linear System with Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanke Zhong ◽  
Tefang Chen
Keyword(s):  
Linear System ◽  
Linear Matrix Inequality ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Robust Observer ◽  
Slack Variable

This paper is concerned with the design of a robust observer for the switched positive linear system with uncertainties. Sufficient conditions of building a robust observer are established by using the multiple copositive Lyapunov-krasovskii function and the average dwell time approach. By introducing an auxiliary slack variable, these sufficient conditions are transformed into LMI (linear matrix inequality). A numerical example is given to illustrate the validities of obtained results.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

Nonlinear Position Control of Digital Hydraulic Cylinder Despite Disturbance

2014 ◽  
Vol 998-999 ◽  
pp. 638-641
Author(s):  
Shi Jie Xu ◽  
J.F. Xing ◽  
Li Kun Peng
Keyword(s):  
Control System ◽  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Nonlinear Model ◽  
Position Control ◽  
Hydraulic Cylinder ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Nonlinear Controller ◽  
Position Control System

A nonlinear controller is presented for a digital hydraulic cylinder against disturbance. We first establish the nonlinear model of digital hydraulic cylinder position control system. Then a Lyapunov function and a nonlinear controller are presented. The controller designing problem is translated into the problem of solving a linear matrix inequality. The experiment results show that the controller proposed by this paper has much better performance than traditional one.

scholarly journals Construction of Lyapunov Function for Power System based on Solving Linear Matrix Inequality

2005 ◽  
Vol 125 (5) ◽  
pp. 461-468
Author(s):  
Atsushi Ishigame ◽  
Hiromu Sakaguchi ◽  
Jun Takashima ◽  
Shirou Suzaki
Keyword(s):  
Lyapunov Function ◽  
Power System ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality

scholarly journals Robust H∞ control of an uncertain bilateral teleoperation system using dilated LMIs

2021 ◽  
pp. 014233122110490
Author(s):  
Bilal Gormus ◽  
Hakan Yazici ◽  
İbrahim Beklan Küçükdemiral
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
State Feedback ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Slave System ◽  
Bilateral Teleoperation ◽  
Reference Tracking ◽  
Teleoperation System ◽  
Force Reflection

A robust state-feedback [Formula: see text] controller is proposed for an uncertain bilateral teleoperation system having norm-bounded parametric uncertainties on mass and damping coefficients of the considered master/slave system. The proposed method ensures robust stability and successful reference tracking and force reflection performance. While Lyapunov stability is used to ensures asymptotic stability, the [Formula: see text] norm from exogenous input to the controlled output is utilized in satisfying the reference tracking and force reflection. As two performance objectives and robust stability requirement are conflicting with each other, the proposed controller reduces the associated conservatism with dilated linear matrix inequalities. Standard and dilated linear matrix inequality-based robust [Formula: see text] state-feedback controllers are performed with a one degree of freedom uncertain master/slave system under reference signal and environmental-induced exogenous force. Numerical simulation results show that the dilated linear matrix inequality-based [Formula: see text] control satisfies lower [Formula: see text] norm than a standard [Formula: see text] control. Moreover, the proposed controller demonstrates a very successful performance in achieving performance objectives despite the stringent norm-bounded parameter uncertainties.

scholarly journals A Reconstruction Procedure Associated with Switching Lyapunov Function for Relaxing Stability Assurance of T-S Fuzzy Mode

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yau-Tarng Juang ◽  
Chih-Peng Huang ◽  
Chung-Lin Yan
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Fuzzy Model ◽  
Alternative Form ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
State Variables ◽  
Stability Criteria ◽  
Quadratic Lyapunov Function ◽  
Reconstruction Procedure

This paper proposes a novel reconstruction procedure to lessen the conservatism of stability assurance of T-S Fuzzy Mode. By dividing the state variables into some bounded regions, the considered T-S fuzzy model can be first transferred to an alternative form via a reconstructing procedure. Thus, we can attain some relaxing stability criteria based on the switching quadratic Lyapunov function (SQLF) method. Notably, these proposed conditions are explicitly formulated by linear matrix inequality (LMI) form and can handily be evaluated by current software tools. Finally some illustrative examples are given to experimentally demonstrate the validity and merit of the proposed method.

scholarly journals Linear Matrix Inequality Based Synthesis Of Pi Controllers For Pmsm With Uncertain Parameters

2018 ◽  
Vol 23 (3) ◽  
pp. 1-10
Author(s):  
Gustavo Guilherme Koch ◽  
Thieli Smidt Gabbi ◽  
Rodrigo Padilha Vieira ◽  
Humberto Pinheiro ◽  
Thiago Araújo Bernardes ◽  
...  
Keyword(s):  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Pi Controllers
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