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A General-Purpose and Programmable Solver for Coupled Matrix Equations
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DOI：10.1109/TCASAI.2025.3640085.png)
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Abstract
En 中文
Coupled matrix equations (CMEs) is a powerful mathematical tool in engineering. Most existing algorithms for solving CMEs rely on digital iterative implementations, which require a significant number of computational steps and time. Moreover, different types of CMEs solving algorithms are not universally applicable or require conversion into linear matrix equations for solving. This paper presents a general and programmable analog computational circuit for solving CMEs to address this. It simultaneously solves all unknown matrices in the CMEs with microsecond-level computation speed and requires only a single-step solution without iteration. It also supports solving any type of CMEs without redesigning the circuit structure. Pspice simulation results show that the average accuracy of the proposed circuit exceeds 98%. The final application validation in the stability determination of Markov jump systems (MJSs) demonstrates that the proposed circuit provides a two orders of magnitude speed advantage.
Keywords:
Mathematical models
Jacobian matrices
Artificial intelligence
Voltage
Time complexity
Accuracy
Operational amplifiers
Matrix converters
Linear systems
Iterative algorithms
Memristor
circuit design
analog computing
general-purpose
coupled matrix equations
Journal
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