On relay control for discrete time systems using linear matrix inequalities

2014 ◽  
Author(s):  
Srinath Govindaswamy ◽  
Laurentiu Hetel ◽  
Andrey Polyakov ◽  
Thierry Floquet
Keyword(s):  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Relay Control ◽  
Discrete Time Systems ◽  
Time Systems

Robust Control Design for Retarded Discrete-Time Systems

2006 ◽  
Vol 129 (1) ◽  
pp. 72-76 ◽  
Author(s):  
El Houssaine Tissir
Keyword(s):  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Synthesis Methods ◽  
Matrix Inequalities ◽  
Stabilizing Controller ◽  
Discrete Time Systems ◽  
Robust Control Design ◽  
Time Systems

This paper focuses on the analysis and synthesis of a robust stabilizing controller for linear discrete time systems with norm-bounded time varying uncertainties. Delay independent robust stability conditions are derived and two synthesis methods are presented. One method is to construct a robust memoryless state feedback control law from the solutions of linear matrix inequalities. The other method consists of designing robust observer-based output feedback controller. The results are expressed in termes of linear matrix inequalities. A comparison with μ∕LDI tests is presented. Furthermore, numerical examples are given for illustration.

scholarly journals Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

2020 ◽  
Vol 48 (4) ◽  
pp. 633-659
Author(s):  
Daniel Bankmann ◽  
Volker Mehrmann ◽  
Yurii Nesterov ◽  
Paul Van Dooren
Keyword(s):  
Discrete Time ◽  
Transfer Functions ◽  
Convex Set ◽  
Solution Set ◽  
Linear Matrix ◽  
Analytic Center ◽  
Matrix Equations ◽  
Matrix Inequalities ◽  
Discrete Time Systems ◽  
Time Systems

AbstractIn this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.

EXPERIMENTAL RESULTS ON CHUA'S CIRCUIT ROBUST SYNCHRONIZATION VIA LMIs

2007 ◽  
Vol 17 (09) ◽  
pp. 3199-3209 ◽  
Author(s):  
C. D. CAMPOS ◽  
R. M. PALHARES ◽  
E. M. A. M. MENDES ◽  
L. A. B. TORRES ◽  
L. A. MOZELLI
Keyword(s):  
Discrete Time ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Chua’S Oscillator ◽  
Laboratory Setup ◽  
Robust Synchronization ◽  
Discrete Time Systems ◽  
Main Ideas ◽  
Time Systems

This paper investigates the synchronization of coupled chaotic systems using techniques from the theory of robust [Formula: see text] control based on Linear Matrix Inequalities. To deal with the synchronization of a class of Lur'e discrete time systems, a project methodology is proposed. A laboratory setup based on Chua's oscillator circuit is used to demonstrate the main ideas of the paper in the context of the problem of information transmission.

scholarly journals LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
A. Hmamed ◽  
M. Alfidi ◽  
A. Benzaouia ◽  
F. Tadeo
Keyword(s):  
Lyapunov Function ◽  
Robust Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Polytopic Uncertainty ◽  
Matrix Inequalities ◽  
Discrete Time Systems ◽  
Parameter Dependent ◽  
Time Systems

Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results.

scholarly journals Optimal guaranteed cost filtering for Markovian jump discrete-time systems

2004 ◽  
Vol 2004 (1) ◽  
pp. 33-48 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Peng Shi
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Estimation Error ◽  
Linear Matrix ◽  
State Estimator ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Discrete Time Systems ◽  
Linear State ◽  
Time Systems

This paper develops a result on the design of robust steady-state estimator for a class of uncertain discrete-time systems with Markovian jump parameters. This result extends the steady-state Kalman filter to the case of norm-bounded time-varying uncertainties in the state and measurement equations as well as jumping parameters. We derive a linear state estimator such that the estimation-error covariance is guaranteed to lie within a certain bound for all admissible uncertainties. The solution is given in terms of a family of linear matrix inequalities (LMIs). A numerical example is included to illustrate the theory.

scholarly journals Finite-Time Bounded Tracking Control for Linear Discrete-Time Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Fucheng Liao ◽  
Yingxue Wu ◽  
Xiao Yu ◽  
Jiamei Deng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Tracking Control ◽  
Original System ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Error System ◽  
Finite Time Boundedness ◽  
Boundedness Problem ◽  
Time Systems

A finite-time bounded tracking control problem for a class of linear discrete-time systems subject to disturbances is investigated. Firstly, by applying a difference method to constructing the error system, the problem is transformed into a finite-time boundedness problem of the output vector of the error system. In fact, this is a finite-time boundedness problem with respect to the partial variables. Secondly, based on the partial stability theory and the research methods of finite-time boundedness problem, a state feedback controller formulated in form of linear matrix inequality is proposed. Based on this, a finite-time bounded tracking controller of the original system is obtained. Finally, a numerical example is presented to illustrate the effectiveness of the controller.

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