High-order Zames-Falb multiplier analysis using linear matrix inequalities

2013 ◽  
Author(s):  
Matthew C. Turner ◽  
Jorge Sofrony
Keyword(s):  
Linear Matrix Inequalities ◽  
High Order ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Multiplier Analysis

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.

Robust Electric Power System Controllers Synthesized on the Basis of Linear Matrix Inequalities

2018 ◽  
Vol 10 (10) ◽  
pp. 4-19
Author(s):  
Magomed G. GADZHIYEV ◽  
◽  
Misrikhan Sh. MISRIKHANOV ◽  
Vladimir N. RYABCHENKO ◽  
◽  
...  
Keyword(s):  
Power System ◽  
Electric Power ◽  
Linear Matrix Inequalities ◽  
Electric Power System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Power System Controllers

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.

scholarly journals Contractors and Linear Matrix Inequalities

2015 ◽  
Vol 1 (3) ◽  
Author(s):  
Jeremy Nicola ◽  
Luc Jaulin
Keyword(s):  
Fixed Point ◽  
Large Class ◽  
Linear Matrix Inequalities ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Constraints ◽  
Linear Matrix ◽  
Nonlinear Constraints ◽  
Matrix Inequalities ◽  
Convex Constraints

Linear matrix inequalities (LMIs) comprise a large class of convex constraints. Boxes, ellipsoids, and linear constraints can be represented by LMIs. The intersection of LMIs are also classified as LMIs. Interior-point methods are able to minimize or maximize any linear criterion of LMIs with complexity, which is polynomial regarding to the number of variables. As a consequence, as shown in this paper, it is possible to build optimal contractors for sets represented by LMIs. When solving a set of nonlinear constraints, one may extract from all constraints that are LMIs in order to build a single optimal LMI contractor. A combination of all contractors obtained for other non-LMI constraints can thus be performed up to the fixed point. The resulting propogation is shown to be more efficient than other conventional contractor-based approaches.

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