Abstract: In this article a method of designing discrete sliding-mode guidance laws is proposed based on the discrete form of the targetmissile relative motion equation in plane. A discrete sliding-mode guidance law is presented which is similar to the discrete form of the continuous time adaptive sliding-mode guidance law. Furthermore, another discrete sliding-mode law is designed which requires just knowing the possible variation range of target normal acceleration between two adjacent sampling instants rather than the target normal acceleration bound. This design significantly reduces system chattering and also suggests a method to estimate target normal acceleration. It is theoretically proved that the two preceding discrete sliding-mode guidance laws are finite time convergent. The quasi sliding-mode switching scope of the discrete sliding-mode guidance laws is discussed; meanwhile a method to calculate the terminal miss distance of discrete sliding-mode guidance laws is presented. The effectiveness of the above results is verified by simulating a space interception process.

Key words: guidance law, discrete sliding-mode control, finite time convergence, quasi sliding-mode, miss distance