Design method of random system tracking controller with multiplicative noise and time delay

The invention discloses a design method of a tracking controller of a random system with multiplicative noise and time delay. A discrete linear system model with an observation function is used for describing a random system which is changed due to sudden environmental disturbance, equipment faults and the like and has multiplicative noise and input time delay, and an augmented system model related to a reference track is established by using an augmented matrix method. Under the condition of a limited time domain, an optimal tracking controller design scheme related to states and reference tracks is provided based on a new maximum value principle, a differential Riccati equation and a Lyapunov theory. In addition, under the condition of infinite time domain, an optimal tracking controllerdesign method capable of enabling the system to be stable is provided according to the Lyapunov stability theory and the algebraic Riccati equation, so that the stability of the system is ensured, and good tracking performan