Analysis and design of linear time-varying systems based on a finite-time performance index

In this paper, the performance analysis and control design problem are considered for a linear time-varying(LTV) system with non-zero initials and energy bounded external disturbance in a finite-time horizon. A finite-time performance index is proposed to be used as a performance metric of such a class of systems which are not required to be stable and with zero initials in the worst-case. The properties and performance criterion of the finite-time performance index are proved and its statistical interpretation is given as well. Then, the design problem of a linear time-varying system is treated based on the proposed finite-time performance index via both state feedback and output feedback. Finally, we apply the proposed approach to the guidance law design problem of a terminal guidance system, which is a typical finite-time system and also the motivation of this work. Simulation experiments are carried out to show the effectiveness of the proposed approach.