Finite-time l2−l∞l2−l∞ tracking control for Markov jump repeated scalar nonlinear systems with partly usable model information

This paper studies the problem of finite-time l2−l∞l2−l∞ tracking control for Markov jump repeated scalar nonlinear systems with partly usable model information. The partly usable model information is considered following a certain Bernoulli distributed white noise sequence. The objective of the study is to design a state-feedback controller such that the augmented closed-loop system is mean-square stochastically finite-time bounded, and a tracking performance level is achieved over a finite time interval. By using the mode-dependent diagonally dominant Lyapunov function approach, some sufficient conditions are established for the existence of an admissible state-feedback controller. Based on these, a state-feedback controller can be constructed by using a simple matrix decoupling approach. Two numerical examples and a modified general economic model are presented to demonstrate the effectiveness of our proposed approach.