Linear constant system based on LMI means that no matter when input is added, as long as the input waveform is the same, the output response waveform of the system is always the same. In such a system, the fault can be diagnosed by linear matrix inequality (LMI). The fault-tolerant control enables the system to compensate the influence of the fault automatically in case of failure to maintain the stability of the system and recover the performance before the system failure as much as possible, so as to ensure the stability and reliability of the system. This is true for real systems, especially those that require high reliability. After the fault, according to Lyapunov stability and Schur complement lemma is an important method to improve the system reliability and reduce the risk of accidents, the fault can be diagnosed by linear matrix inequality (LMI). This method is an important method to improve the reliability of the system and reduce the risk of accidents. It is also important to make the system return to normal quickly after fault diagnosis. Based on sliding mode control, a fault-tolerant controller is designed to ensure the stable operation of the system.<br>
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