Design and Application of Programmable Analog Circuit for Solving Lyapunov Matrix Equation Based on Memristors

The Lyapunov matrix equation is widely used in scientific computing and engineering applications; how to quickly solve the Lyapunov matrix equation has been an urgent requirement in the era of big data and Internet of Things. However, the related work of the hardware circuits performing effective analog computing for solving the above problem is hardly present in the existing literature. Aiming at this problem, for the first time, we propose an analog programmable circuit for solving the Lyapunov matrix equation based on memristors to the best of our knowledge. This article gives the architecture of circuits, which can solve the Lyapunov matrix equation of any order for continuous and discrete systems. Moreover, adjusting the conductance of memristors and input current source can achieve programmable function. The evaluation shows that the average computing accuracy is over 98%, the computing time is three orders of magnitude faster than computer simulation, and the accuracy can still exceed 92% even with 10% error interference compared to digital processors. The circuit has significant advantages in power consumption compared to traditional digital processors.