Optimal state regulator analysis for discrete-time LTI systems: A subregion control approach

This paper presents state regulation analysis for discrete-time LTI systems. Based on state 2-norm, the decreasing and non-overshooting regions are defined, and some key properties are discussed first. Later, all discrete-time LTI systems are classified into four categories depending on their state 2-norm monotonous properties, and a deep region partition is carried out for the fourth category systems, which is in the majority and the most complex cases. An example is given to illustrate the theory results at last.