Partial stability of some guidance dynamic systems with delayed line-of-sight angular rate

Abstract

In this paper, for a class of the guidance dynamic system proposed by Moon, Kim, and Kim (Journal of Guidance, Control and Dynamics, vol. 24, no. 4, pp. 659–664, 2001) and Shafiei and Binazadeh (ISA Transactions, vol. 51, pp. 298–303, 2012), a new nonlinear missile guidance law with delayed line-of-sight (LOS) angular rate is introduced, and then partial stability is studied by using the method of Lyapunov functionals and stability theory of functional differential equations. The time delay in the LOS angular rate comes from the missile guidance dynamic system in which a low-cost sensor is used to obtain LOS rate information by image processing techniques. Furthermore, for a class of classical proportional navigation control system with delayed line-of-sight rate studied by Dhananjay, Lum, and Xu (IEEE Transactions on Control Systems Technology, vol. 21, pp. 247–253, 2013), a new stability region is obtained by using the method of Lyapunov-Razumikhin.