Analysis and design of discrete-time linear systems with nested actuator saturations

• Published in: Systems & control letters Vol. 62; no. 10; pp. 871 - 879
• Main Author: Zhou, Bin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2013
• Subjects: Attraction; Constrained control; Control systems; Convex hull; Convex sets; Design engineering; Dynamical systems; Invariant sets; Linear systems; Mathematical analysis; Mathematical models; Nested saturations; Saturation; Saturation nonlinearity; Convex sets; Convex hull; Nested saturations; Invariant sets; Constrained control; Saturation nonlinearity
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2013.06.012

This paper is concerned with the analysis and design of discrete-time linear systems subject to nested saturation functions. By utilizing a new compact convex hull representation of the saturation nonlinearity, a linear matrix inequalities (LMIs) based condition is obtained for testing the local and global stability of the considered nonlinear system. The estimation of the domain of attraction and the design of feedback gains such that the estimation of the domain of attraction for the resulting closed-loop system is maximized are then converted into some LMIs based optimization problems. Compared with the existing results on the same problems, the proposed solutions are less conservative as more slack variables are introduced into the conditions. A couple of numerical examples are worked out to validate the effectiveness of the proposed approach.