Perturbation Analysis of the Continuous-time Regional Pole Assignment and H2 Performance Control Problems: an LMI Approach

2014 ◽  
Vol 12 (3-4) ◽  
pp. 28-35
Author(s):  
A. Yonchev
Keyword(s):  
Perturbation Analysis ◽  
Continuous Time ◽  
Pole Assignment ◽  
Linear Matrix ◽  
Control Problems ◽  
Matrix Inequalities ◽  
Performance Control ◽  
Hand Part ◽  
And Performance ◽  
Time Systems

Abstract In the paper a method to conduct perturbation analysis of regional pole assignment and H2 performance control problems for linear continuous-time systems are investigated. The studied control problems are based on solving LMIs (Linear Matrix Inequalities) and applying Lyapunov functions. The problem of performing sensitivity analysis of the perturbed matrix inequalities is done in a similar way as for perturbed matrix equations, after introducing a slightly perturbed right hand part. The calculated perturbation bounds can be used to analyze the feasibility and performance of the considered control problems in presence of perturbations in the system and the controller. An illustrative numerical example is also discussed in this paper.

scholarly journals Observer-based fault estimation for linear systems with distributed time delay

2013 ◽  
Vol 23 (2) ◽  
pp. 169-186 ◽  
Author(s):  
Anna Filasová ◽  
Daniel Gontkovič ◽  
Dušan Krokavec
Keyword(s):  
Time Delay ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Structured Matrix ◽  
Continuous Time Systems ◽  
Distributed Time Delay ◽  
And Performance ◽  
Time Systems

The paper is engaged with the framework of designing adaptive fault estimation for linear continuous-time systems with distributed time delay. The Lyapunov-Krasovskii functional principle is enforced by imposing the integral partitioning method and a new equivalent delaydependent design condition for observer-based assessment of faults are established in terms of linear matrix inequalities. Asymptotic stability conditions are derived and regarded with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. Simulation results illustrate the design approach, and demonstrates power and performance of the actuator fault assessment.

scholarly journals An Improved Antiwindup Design Using an Anticipatory Loop and an Immediate Loop

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qing Wang ◽  
Maopeng Ran ◽  
Chaoyang Dong ◽  
Maolin Ni
Keyword(s):  
Linear Matrix Inequalities ◽  
Continuous Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
The Other ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Continuous Time Systems ◽  
Linear Invariant ◽  
Time Systems

We present an improved antiwindup design for linear invariant continuous-time systems with actuator saturation nonlinearities. In the improved approach, two antiwindup compensators are simultaneously designed: one activated immediately at the occurrence of actuator saturation and the other activated in anticipatory of actuator saturation. Both the static and dynamic antiwindup compensators are considered. Sufficient conditions for global stability and minimizing the inducedL2gain are established, in terms of linear matrix inequalities (LMIs). We also show that the feasibility of the improved antiwindup is similar to the traditional antiwindup. Benefits of the proposed approach over the traditional antiwindup and a recent innovative antiwindup are illustrated with well-known examples.

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.

Harmony search optimization for robust pole assignment in union regions for synthesizing feedback control systems

2017 ◽  
Vol 40 (6) ◽  
pp. 1956-1969 ◽  
Author(s):  
Junchang Zhai ◽  
Liqun Gao ◽  
Steven Li
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Search Algorithm ◽  
Harmony Search ◽  
Pole Assignment ◽  
Harmony Search Algorithm ◽  
Time System ◽  
Feedback Control Systems ◽  
Time Systems

This paper is concerned with robust pole assignment optimization for synthesizing feedback control systems via state feedback or observer-based output feedback in specified union regions using the harmony search algorithm. By using exact pole placement theory and the harmony search algorithm, robust pole assignment for linear discrete-time systems or linear continuous-time systems in union regions can be converted into a global dynamical optimization problem. The robust measured indices are derived for robust union region stability constraints and a robust [Formula: see text] performance. For the nonlinear, robust measured indices, a set of dynamic poles and the corresponding feedback controllers can be obtained by global dynamic optimization based on the harmony search algorithm and the idea of robust exact pole assignment. One key merit of the proposed approach is that the radius or the position of the sub-regions can be arbitrarily specified according to the transient performance request. Furthermore, the eigenstructure of the closed-loop system matrix can be optimized with better robustness for the proposed approach. Finally, the simulation results for a discrete-time system and a continuous-time system demonstrate the effectiveness and superiority of the proposed method.

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.

Admissible Conditions for T-S Fuzzy Descriptor Systems with Non-Differentiable Membership Functions

2013 ◽  
Vol 415 ◽  
pp. 259-266
Author(s):  
Peng Lin ◽  
Gang Hu
Keyword(s):  
Continuous Time ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Structural Information ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Membership Functions ◽  
Matrix Inequalities ◽  
Closed Loop Systems ◽  
Takagi Sugeno

In this paper, the admissible conditions (regular, impulse-free and stable) for a class of continuous-time Takagi-Sugeno (T-S) fuzzy descriptor systems are investigated. Sufficient admissible conditions for the closed-loop systems under non-parallel distributed compensation (non-PDC) feedback are proposed. This approach is mainly based on the state space division properly to make the membership functions continuous differentiable. Moreover, in order to make good use of the systems’ structural information in rules, the provided conditions are obtained through fuzzy Lyapunov functions candidate and can be formulated in terms of dilated Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed approach is shown through numerical example by using the optimization toolbox.

scholarly journals Sufficient Dilated LMI Conditions for Static Output Feedback Robust Stabilization of Linear Continuous-Time Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Kamel Dabboussi ◽  
Jalel Zrida
Keyword(s):  
Output Feedback ◽  
Continuous Time ◽  
Robust Stabilization ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Slack Variables ◽  
Continuous Time Systems ◽  
Time Systems ◽  
Static Output

New sufficient dilated linear matrix inequality (LMI) conditions for the static output feedback control problem of linear continuous-time systems with no uncertainty are proposed. The used technique easily and successfully extends to systems with polytopic uncertainties, by means of parameter-dependent Lyapunov functions (PDLFs). In order to reduce the conservatism existing in early standard LMI methods, auxiliary slack variables with even more relaxed structure are employed. It is shown that these slack variables provide additional flexibility to the solution. It is also shown, in this paper, that the proposed dilated LMI-based conditions always encompass the standard LMI-based ones. Numerical examples are given to illustrate the merits of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document