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Dynamic neural network models trained by the proposed P2PEDLL based on matrix inequality formulation are exponentially stable, with a guaranteed exponential peak-to-peak norm performance.
Based on matrix inequality formulation with a fixed parameter, the proposed learning law can be designed by solving two matrix inequalities, which can be checked easily using standard numerical software [27, 28].
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First, sufficient delay-dependent stability criteria are derived by choosing a Lyapunov-Krasovskii functional candidate based on matrix inequalities for a stabilizing H∞ synthesis.
We introduce some new relative efficiency criteria and their lower or upper bounds are given based on matrix norm inequalities in Theorem 3.1, Theorem 3.2 and Theorem 3.3.
Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented, which guarantees the estimation error systems are stochastically admissible and achieve a prescribed H∞ noise attenuation performance index.
Moreover, by using the Lyapunov Krasovskii functional (LKF) method, stochastic analysis technique and matrix theory, a sufficient condition based on linear matrix inequality is obtained, thus the drive system can synchronize the response system.
Its design is based on linear matrix inequality (LMI) technique.
An iterative algorithm based on linear matrix inequality (LMI) is given to obtain the solutions.
Based on linear matrix inequality (LMI) approach, a delay-dependent stability criteria has been developed.
Based on linear matrix inequality (LMI), state feedback controller H2 and H∞ with constraints is illustrated.
Sufficient conditions for exponential stabilization for the closed-loop system are given based on linear matrix inequality theory.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com