Dynamic system methods for solving mixed linear matrix inequalities and linear vector inequalities and equalities |
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Authors: | Xiaolin Hu |
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Institution: | State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology (TNList), Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China |
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Abstract: | A novel idea is proposed for solving a system of mixed linear matrix inequalities and linear vector inequalities and equalities. First, the problem is converted into an unconstrained minimization problem with a continuously differentiable convex objective function. Then, a continuous-time dynamic system and a discrete-time dynamic system are proposed for solving it. Under some mild conditions, the proposed dynamic systems are shown to be globally convergent to a solution of the problem. The merits of the methods refer to their simple numerical implementations and capability for handling nonstrict LMIs easily. In addition, the methods are promising in neural circuits realization, and therefore have potential applications in many online control problems. Several numerical examples are presented to illustrate the performance of the methods and substantiate the theoretical results. |
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Keywords: | Dynamic system Linear matrix inequality (LMI) Semidefinite programming Recurrent neural network Stability analysis |
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