Linear M RAW Synthesis

2011 ◽  
Author(s):  
Luca Zaccarian ◽  
Andrew R. Teel
Keyword(s):  
Global Stability ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Feedback Signal ◽  
Regional Stability ◽  
Performance Properties ◽  
Response Recovery ◽  
And Performance ◽  
The Stability ◽  
Compensation Signal

This chapter deals with linear model recovery anti-windup (MRAW) synthesis. The MRAW structure permits recovering information about the unconstrained response, so that unconstrained response recovery is possible through the extra degree of freedom represented by the unspecified compensation signal. The stability and performance properties induced by MRAW on the closed loop depend on the choice of the feedback signal. In discussing linear MRAW synthesis, the chapter refers to suitable state–space representations of the plant and of the anti-windup compensator dynamics. It first considers anti-windup synthesis algorithms based on linear matrix inequalities (LMIs) for which global stability and performance are guaranteed before describing LMI-based synthesis algorithms for regional stability and performance.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

Gobal Optimization Based Power System Stablization with WAMS Time Delay Study

2012 ◽  
Vol 433-440 ◽  
pp. 7362-7367
Author(s):  
Zhang Lin ◽  
Di Chen Liu ◽  
Wu Jun ◽  
Qing Fen Liao ◽  
Yun Lei ◽  
...  
Keyword(s):  
Global Optimization ◽  
Time Delay ◽  
Power System ◽  
Low Frequency ◽  
System Stability ◽  
Area Measurement ◽  
Wide Area ◽  
Linear Matrix ◽  
Feedback Signal ◽  
The Stability

It is very important to take into consideration time delay in wide area power system stability; the design of PSS (Power System Stabilizer) should consider global optimization with WAMS (Wide Area Measurement System) time delay. Newly designed PSS should be insensitive to time delay and suppress internal low frequency oscillations. It is used as feedback signal and is real-time synchronous that WAMS signal shows. Power system is modeled with the consideration of time delay. LMI (Linear Matrix Inequalities) is used to solve the stability condition of time delay system. Based on the time-delay effect of the wide-area measurement signals, this paper redesigned the PSS with global optimization of power system. The attached two-area-four-machine system simulation illustrates that wide-area PSS designed by global optimization with the consideration of time-delay can limit internal low frequency oscillation with time-delay insensitivity, and improve the stability of power system. It implements global optimization of PSS with WAMS time delay stability.

scholarly journals On the stability of 2D general Roesser Lyapunov systems

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 85-97
Author(s):  
Mohammed Amine Ghezzar ◽  
Djillali Bouagada ◽  
Kamel Benyettou ◽  
Mohammed Chadli ◽  
Paul Van Dooren
Keyword(s):  
Asymptotic Stability ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
The Stability

This paper addresses the problem of stability for general two-dimensional (2D) discrete-time and continuous-discrete time Lyapunov systems, where the linear matrix inequalities (LMI's) approach is applied to derive a new sufficient condition for the asymptotic stability.

Linear Matrix Inequalities in Stability Problems: Retrospective and Theoretical Aspects

2019 ◽  
Vol 20 (11) ◽  
pp. 643-654
Author(s):  
V. A. Kamenetskiy
Keyword(s):  
Numerical Methods ◽  
Programming Problem ◽  
Linear Matrix Inequalities ◽  
Gradient Algorithm ◽  
Linear Matrix ◽  
Convex Programming Problem ◽  
Matrix Inequalities ◽  
Famous Book ◽  
Semidefinite Programming Problem ◽  
The Stability

Some aspects of the development of the theory of linear matrix inequalities are considered. A number of results obtained at the initial stage of the development of this theory, both in the development of numerical methods and in obtaining analytical conditions for their solvability, are highlighted. The main attention is focused on the system of linear matrix inequalities arising in solving the absolute stabi lity problem. E. S. Pyatnitskiy and his followers showed that the solvability of this system is a criterion for the existence of a quadratic Lyapunov function and a sufficient condition for absolute stability. The prerequisites leading to this result are considered here. The use of the considered system of inequalities for studying the stability of hybrid systems described by differential inclusions and switching systems is shown. An analysis is given of citing some works of Pyatnitskiy’s school on the theory of stability and the theory of systems of linear matrix inequalities, from which the relevance of the results of these works at the present time follows.In developing numerical methods, it was first shown in the work of Pyatnitskiy and Skorodinskiy that the solvability problem for a system of linear matrix inequalities reduces to a convex programming problem. An interesting gradient algorithm for finding solutions to such a system is also presented. In analyzing analytical conditions of solvability, an unsolvability criterion for the system of our interest obtained by Kamenetskiy and Pyatnitskiy is noted. In modern terms, this result can be considered as a description of an admissible set in the dual semidefinite programming problem. A similar result is given in the famous book by S. Boyd et al. The paper shows that the result of Boyd et al. is a simple corollary of the unsolvability criterion. Here the unsolvability criterion is generalized and refined.

An LMI-Based Hedging Approach to Model Reference Adaptive Control With Actuator Dynamics

2015 ◽  
Author(s):  
Benjamin C. Gruenwald ◽  
Daniel Wagner ◽  
Tansel Yucelen ◽  
Jonathan A. Muse
Keyword(s):  
Dynamical System ◽  
Adaptive Control ◽  
Linear Matrix Inequalities ◽  
Model Reference Adaptive Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Model Reference ◽  
Actuator Dynamics ◽  
The Stability ◽  
Model Reference Adaptive

Although model reference adaptive control has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, an linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that does not get affected due to the presence of actuator dynamics. Specifically, we first generalize the hedging approach to cover cases in which actuator output and is known and unknown. We next show the stability of the closed-loop dynamical system using tools from Lyapunov stability and linear matrix inequalities. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed linear matrix-inequalities-based hedging approach to model reference adaptive control.

scholarly journals Robust Control for Helicopters Performance Improvement: an LMI Approach

2020 ◽  
Author(s):  
Luiz Ricardo Trajano da Silva ◽  
Victor Augusto Fernandes de Campos ◽  
Alain Segundo Potts
Keyword(s):  
Linear Matrix ◽  
Linear Quadratic ◽  
Performance Requirements ◽  
Multiple Input ◽  
Polytopic Systems ◽  
And Performance ◽  
The Stability ◽  
Linearized Model ◽  
Multivariate Systems ◽  
Lmi Region

This paper presents an LMI (Linear Matrix Inequalities) application for the design of robust controllers for multivariate systems that have multiple points of operation. Some systems change their parameters along time, then, it is necessary to switch the control for different operational points. The purpose of this controller is to ensure the stability and performance requirements of the system for different operating points with the same controller. The method uses the following concepts of predefined structures controller, LMI region, and polytopic systems. To validate the controller a linearized model of a helicopter was used. These helicopters belong to a system class of MIMO (Multiple-Input Multiple Outputs) type and present a complex dynamic in their flight modes, therefore, due to these features, this type of helicopter is a good model to implement and test the efficiency of the described method in this work. The results were satisfactory. Some limitations in its implementation were found and discussed. An LQG (Linear-Quadratic-Gaussian) controller was also designed for the same model of the helicopter just for comparison. Analyzing the settling time properties, the LMI controller presented a better response than the LQG controller.

scholarly journals Repetitive Processes Based Iterative Learning Control Designed by LMIs

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jamel Dridi ◽  
Selma Ben attia ◽  
Salah Salhi ◽  
Mekki Ksouri
Keyword(s):  
Linear Matrix Inequalities ◽  
Iterative Learning Control ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequalities ◽  
Repetitive Processes ◽  
Linear Repetitive Processes ◽  
Control Schemes ◽  
The Stability ◽  
Repetitive Systems

This paper addressed the stability analysis along the pass and the synthesis problem of linear 2D/repetitive systems. The algorithms for control law design are developed using a strong form of stability for discrete and differential linear repetitive processes known as stability along the pass. In particular, recent work on the use of linear matrix inequalities- (LMIs-) based methods in the design of control schemes for discrete and differential linear repetitive processes will be highlighted by the application of the resulting theory of linear model. The resulting design computations are in terms of linear matrix inequalities (LMIs). Simulation results demonstrate the good performance of the theoretical scheme.

A Model Reference Adaptive Control Framework for Uncertain Dynamical Systems With High-Order Actuator Dynamics and Unknown Actuator Outputs

2017 ◽  
Author(s):  
Benjamin C. Gruenwald ◽  
K. Merve Dogan ◽  
Tansel Yucelen ◽  
Jonathan A. Muse
Keyword(s):  
Adaptive Control ◽  
Linear Matrix Inequalities ◽  
High Order ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Model Reference ◽  
Adaptive Controllers ◽  
Actuator Dynamics ◽  
The Stability ◽  
Model Reference Adaptive

As it is well-known, the stability properties of model reference adaptive controllers can be seriously affected by the presence of actuator dynamics. To this end, the authors recently proposed linear matrix inequalities-based hedging approaches to compute the stability limits of model reference adaptive controllers in the presence of a) scalar actuator dynamics with known outputs, b) scalar actuator dynamics with unknown outputs, and c) high-order (linear time-invariant) actuator dynamics with known outputs. The common denominator of these approaches is that they have the capability to rigorously characterize the fundamental stability interplay between the system uncertainties and the necessary bandwidth of the actuator dynamics. Building on these results, the purpose of this paper is to extend the recent work by the authors to the general case, where there exist high-order actuator dynamics with unknown outputs in the closed-loop model reference adaptive control systems. For this purpose, we propose an observer architecture to estimate the unknown output of the actuator dynamics and use the estimated actuator output to design the linear matrix inequalities-based hedging framework. Remarkably, with the proposed observer, the sufficient stability condition in this case of unknown actuator outputs is identical to the case with known actuator outputs that was established in the prior work by the authors. Therefore, a control designer can utilize the proposed framework for practical applications when the output of the actuator dynamics is not measurable, and hence, unknown (e.g., in hypersonic vehicle applications). An illustrative numerical example complements the proposed theoretical contribution.

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