A design method for fixed-order H/sub /spl infin// controllers via bilinear matrix inequalities

1999 ◽  
Keyword(s):  
Design Method ◽  
Matrix Inequalities ◽  
Bilinear Matrix Inequalities ◽  
Fixed Order

scholarly journals Parameterized Regulator Synthesis for Bimodal Linear Systems Based on Bilinear Matrix Inequalities

2008 ◽  
Vol 2008 ◽  
pp. 1-22 ◽  
Author(s):  
Zhizheng Wu ◽  
Foued Ben Amara
Keyword(s):  
Linear Systems ◽  
Design Method ◽  
Second Step ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Switched Linear System ◽  
Central Controller ◽  
Bilinear Matrix Inequalities ◽  
Synthesis Approach ◽  
Selection Of

A regulator design method is presented for switched bimodal linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. The switching in the bimodal system is defined by a switching surface. The regulator design approach consists of three steps. The first step is based on constructing a switched observer-based state feedback central controller for the switched linear system. The second step involves augmenting the switched central controller with additional dynamics to construct a parameterized set of switched controllers. In the third step, two sufficient regulation conditions are derived for the resulting switched closed loop system. The regulation conditions present guidelines for the selection of the additional dynamics used to parameterize the switched controllers to yield the desired regulator. A regulator synthesis approach is proposed based on solving properly formulated bilinear matrix inequalities. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.

scholarly journals Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Deyi Li ◽  
Yuanyuan Wang ◽  
Guici Chen ◽  
Shasha Zhu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Finite Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Feedback ◽  
Inertial Neural Networks ◽  
Finite Time Stabilization

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

Multi-Model Adaptive Regulation for Aircraft Dynamics With Different Zero Structures

2014 ◽  
Author(s):  
Eric D. Peterson ◽  
Harry G. Kwatny
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Linear Matrix ◽  
Model Design ◽  
Multiple Model ◽  
Matrix Inequalities ◽  
Adaptive Regulation ◽  
Aircraft Dynamics ◽  
Adaptive Regulator ◽  
Parameter Dependent

An adaptive regulator is designed for parameter dependent families of systems subject to changes in the zero structure. Since continuous adaptive regulation is limited by relative degree and right half plane zeros, a multiple model adaptive regulator is implemented. The two multiple model design subproblems, covering and switching, are addressed with LQR state feedback and Lyapunov function switch logic respectively. These two subproblems are combined into a set of Linear Matrix Inequalities (LMI) and concurrently solved. The multiple model design method is applied to longitudinal aircraft dynamics.

Fixed-order ℋ∞ controller design for MIMO systems via polynomial approach

2018 ◽  
Vol 41 (7) ◽  
pp. 1985-1992 ◽  
Author(s):  
Bilal Erol ◽  
Akın Delibaşı
Keyword(s):  
Traditional Method ◽  
Controller Design ◽  
Mimo Systems ◽  
Linear Matrix ◽  
Main Difficulty ◽  
Matrix Inequalities ◽  
Central Polynomial ◽  
Fixed Order ◽  
Inner Approximation ◽  
Associated Solution

This paper presents a fixed-order [Formula: see text]∞ controller design based on linear matrix inequalities for multi-input–multi-output systems. The main difficulty in the development of a fixed-order controller design is that the associated solution set of the problem is defined in a non-convex cluster, and that makes the problem computationally intractable. The convex inner approximation is used to deal with this non-convexity. The proposed controller design approach is applied to some elegant numerical problems taken from various previous works. To show the effectiveness of the proposed method, the full-order [Formula: see text]∞ controller and fixed-order controllers are constructed for these models using the traditional method and popular toolboxes, respectively. Furthermore, in this paper, some strategies for choosing the central polynomial, which is the main conservatism of the proposed method, are discussed.

The Flying Height Control with a Switched Controller for Data Storage Devices

2012 ◽  
Vol 424-425 ◽  
pp. 1159-1163
Author(s):  
Zhi Zheng Wu ◽  
Mei Liu
Keyword(s):  
Data Storage ◽  
Design Method ◽  
Synthesis Method ◽  
Flying Height ◽  
Linear Matrix ◽  
Experimental Setup ◽  
Matrix Inequalities ◽  
Storage Devices ◽  
Height Control ◽  
Stabilizing Controllers

This paper considers the flying height control problem for data storage devices using a switched controller. First, a set of switched -parameterized stabilizing controllers is constructed. Then a sufficient regulation condition for the switched system is obtained, and a regulator synthesis method is derived based on solving a set of properly formulated linear matrix inequalities. Finally, the proposed regulator design method is evaluated on an experimental setup motivated by the flying height regulation problem in data storage devices

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