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Schedule design for nonlinear NCSs
Published in Longo Stefano, Tingli Su, Herrmann Guido, Barber Phil, Optimal and Robust Scheduling for Networked Control Systems, 2018
Longo Stefano, Tingli Su, Herrmann Guido, Barber Phil
Although a variety of techniques have been developed for the design of optimal communication sequences for linear NCSs, the literature for nonlinear NCSs seems to concentrate more on the stability problem (although ℒ2gain stability as in [91] may lead to suitable designs and the work of [98] is an exception for mildly nonlinear systems), and methods for optimal communication design have been somehow ignored [7, 13]. However, computational tools to verify performance and stability of nonlinear systems are nowadays readily available. The semidefinite programming approach has been extended from the linear matrix inequality framework to the idea of sum-of-squares (SOS).
Cooperative Control of Networked Power Systems
Published in Magdi S Mahmoud, Multiagent Systems, 2020
Following the team robust control theory [541], it can be shown that, in minimax team problems with a quadratic cost, linear decisions are optimal and can be found by solving a linear matrix inequality. The reader is referred to [542], with regard to the formalization of the distributed linear quadratic H∞ control problem with information constraints, and to [544], where an optimal distributed controller synthesis for chain structures applied to vehicle formations is proposed. The solution of the problem is demonstrated in the following theorem:
∞ Filtering of Continuous-Time Systems
Published in Frank L. Lewis, Lihua Xie, Dan Popa, Optimal and Robust Estimation, 2017
Frank L. Lewis, Lihua Xie, Dan Popa
The important point to note is that γ(X, Y) is a jointly linear matrix function of X and Y. Thus, the H∞ filter design problem is reduced to a standard convex optimization problem involving a linear matrix inequality. This convex problem can be numerically solved efficiently by interior-point methods. A standard MATLAB package called MATLAB LMI-Toolbox (Gahinet et al. 1995) is available to solve the above problem.
Pole assignment and distributed output feedback control via graph-based decomposition
Published in International Journal of Control, 2023
Pegah Moushaee, Maryam Babazadeh
The distance to uncontrollability or fixed-mode radius is introduced in Eising (1984) to provide a continuous metric for the assessment of controllability. The pair has the guaranteed distance to uncontrollability (with respect to the perturbations such that ) if and only if Alternatively, the distance to uncontrollability is defined as the smallest of the perturbation in which makes the system uncontrollable, In the presence of perturbations in , evaluation of (5) at the eigenvalues of A is no longer permissible. In this case, controllability assessment requires sweeping s over the entire complex plane that is numerically intractable. However, it is possible to derive reliable estimations of the distance to uncontrollability or controllability radius. The next theorem determines the guaranteed distance to uncontrollability by introducing a convex set with linear matrix inequality constraints.
Reduced-order observer-based interval estimation for discrete-time linear systems
Published in Systems Science & Control Engineering, 2021
Yantao Chen, Junqi Yang, Zhenhua Wang, Hongwei Zhang
Under Assumption 3.1, if for a given scalar , there exist a positive definite symmetric matrix and matrix such that the following linear matrix inequality has a feasible solution, then the following system is a robust reduced-order observer of the system (5) with gain matrix . The transfer function from to , , satisfies , where is the state estimation error between the system (16) and reduced-order observer (18), and is the estimation of system state in the case of reduced-order observer.
Outlier-resistant l 2-l ∞ state estimation for discrete-time memristive neural networks with time-delays
Published in Systems Science & Control Engineering, 2021
Peifeng Zhao, Hongjian Liu, Guang He, Derui Ding
Consider DMNNs (1) and let the scalar be given. If there exist a symmetric positive definite matrix a matrix X, and three positive scalars and ς such that following linear matrix inequality holds: where with then the augmented estimation error system (9) is stochastically stable while achieving the - performance constraint. Further, the desired estimator parameter is determined by .