Semi-global output regulation for discrete-time singular linear systems with input saturation via composite nonlinear feedback control

Abstract

The semi-global output regulation problem of multi-variable discrete-time singular linear systems with input saturation is investigated in this paper. A composite nonlinear feedback control law is constructed by using a low gain feedback technique for semi-global stabilisation of discrete-time singular linear systems with input saturation. The sufficient solvability conditions of the semi-global output regulation problem by composite nonlinear feedback control are established. When the composite nonlinear feedback control law is reduced to a linear control law, the solvability conditions are an exact discrete-time counterpart of the semi-global output regulation problem of continuous-time singular linear systems. With the extra control freedom of the nonlinear part in the composite nonlinear feedback control law, the transient performance of the closed-loop system can be improved by carefully choosing the linear feedback gain and the nonlinear feedback gain. The design procedure of the composite nonlinear feedback control law and the improvement of the transient performance are illustrated by a numerical example.

Adaptive output regulation for a class of nonlinear systems with guaranteed transient performance

“…To deal with the constraints related to the transient performance issue, one approach is to employ the composite nonlinear feedback (CNF) technique composed of linear and nonlinear feedback parts. It was first proposed in Lin et al (1998), and recently it has been extensively studied to improve the output regulation performance of linear 1 School of Automation Science and Engineering, South China University of Technology, Guangzhou systems (Zhang and Lan 2013;Lin et al 2017). In consideration of nonlinear systems with constraints, the Barrier Lyapunov Function (BLF) technique has received more and more attention (Tee et al , 2011.…”

Modified composite nonlinear feedback control for output tracking of nonstep signals in singular systems with actuator saturation

“…Moreover, CNF control law has also been studied in the works of Feng and Ho and Jafari and Binazadeh for discrete‐time singular systems. Additionally, semiglobal output regulation in singular systems via the CNF controller has been studied in the work of Lin et al…”

“…Moreover, CNF control law has also been studied in the works of Feng and Ho 34 and Jafari and Binazadeh 35 for discrete-time singular systems. Additionally, semiglobal output regulation in singular systems via the CNF controller has been studied in the work of Lin et al 36 The subject of this article is to modify the CNF controller for output tracking of nonstep reference signals in continuous-time singular systems with input saturation and external disturbances. This issue has not been studied so far to the best of the authors' knowledge.…”

Sampled-data control for nonlinear singular systems based on a Takagi–Sugeno fuzzy model

“…Compared to regular systems, a singular system is more complicated because the stability, regularity and causality or absence of impulses should be considered simultaneously. In recent years, many control problems have been considered for singular systems (Gao et al, 2016; Lin et al, 2017; Lu et al, 2016; Qin et al, 2015; Shi et al, 2016; Wang et al, 2017a, 2017c, 2017d; Wu et al, 2017). For example, the sliding mode control problem is discussed by Wang et al (2017a, 2017c) .…”

“…The H ∞ control problem has been discussed by Qin et al (2015) and Wu et al (2017). The dissipative problem is considered by Shi et al (2016) and Lin et al (2017). The Kalman filtering problem is dealt with by Lu et al (2016).…”