State-Space Region-Invariance of Discrete-Time Control Systems

Abstract

In the paper, the so-called region-invariance properties of discrete-time control systems are considered. An already known notion of positivity of control systems has been generalized (using a kind of geometric insight instead of a pure algebraic approach) to the general nonlinear discrete-time control systems, general regions in state-space, and controls from polyhedral cones in input-space. The class of such control systems has been characterized. Numerous numerical examples illustrating individual cases under consideration are presented in the paper.

Keywords

• Linear and nonlinear discrete-time control systems
• state-space invariance
• positive systems