Indefinite matrix inequalities via matrix means

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.

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Dissipativity analysis of delayed stochastic generalized neural networks with Markovian jump parameters

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0244 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Grienggrai Rajchakit ◽

Ramalingam Sriraman ◽

Rajendran Samidurai

Keyword(s):

Linear Matrix ◽

Time Varying ◽

Matrix Inequalities ◽

Markovian Jump ◽

Stochastic Perturbations ◽

Practical Applications ◽

Markovian Jump Parameters ◽

Generalized Neural Networks ◽

System Information ◽

Dissipativity Analysis

Abstract This article discusses the dissipativity analysis of stochastic generalized neural network (NN) models with Markovian jump parameters and time-varying delays. In practical applications, most of the systems are subject to stochastic perturbations. As such, this study takes a class of stochastic NN models into account. To undertake this problem, we first construct an appropriate Lyapunov–Krasovskii functional with more system information. Then, by employing effective integral inequalities, we derive several dissipativity and stability criteria in the form of linear matrix inequalities that can be checked by the MATLAB LMI toolbox. Finally, we also present numerical examples to validate the usefulness of the results.

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Random Sampling Many-Dimensional Sets Arising in Control

Mathematics ◽

10.3390/math9050580 ◽

2021 ◽

Vol 9 (5) ◽

pp. 580

Author(s):

Pavel Shcherbakov ◽

Mingyue Ding ◽

Ming Yuchi

Keyword(s):

Monte Carlo ◽

Random Sampling ◽

Linear Matrix ◽

Matrix Inequalities ◽

Computational Mathematics ◽

Closed Form Solutions ◽

Monte Carlo Techniques ◽

Control Optimization ◽

Point Representation ◽

Hit And Run

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

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