Guaranteed cost finite-time control of positive switched nonlinear systems with D-perturbation

Abstract

This paper considers the guaranteed cost nite-time boundedness of positive switched nonlinear systems with D-perturbation and time-varying delay. Firstly, the de nition of guaranteed cost nite-time boundedness is introduced. By using the Lyapunov-Krasovskii functional and average dwell time (ADT) approach, an output feedback controller is designed and su cient conditions are obtained to ensure the corresponding closed-loop systems to be guaranteed cost nite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, two examples are provided to show the e ectiveness of the proposed method.

L1 Input‐Output Finite‐Time Control of Positive Switched Nonlinear Systems

“…In an economic system, affected by the national macroeconomic regulation and control policy, the relation between supply and demand always presents nonlinear behavior. So, it is more suitable to describe the price dynamic model by positive switched nonlinear systems [18]. Consider the parameters as follows:…”

“…Reference [17] firstly defined the concept of finite-time stability (FTS) for linear deterministic systems. For positive switched nonlinear systems, only [18] considered the guaranteed cost finite-time control problem. Recently, the definition of input-output finite-time stability (IO-FTS) is proposed in [19], which is fully consistent with the definition of FTS.…”

Asynchronously input-output finite-time control of discrete-time nonlinear impulsive positive switched systems

“…As a special case of positive systems (Anhngoc, 2015; Shen and Chen, 2017; Zhao et al, 2016), the positive switched systems have been paid much attention in that such systems have been founded in many practical fields such as communication networks, viral mutation and formation flying, and so on (Liu and Xiang, 2014; Zhao et al, 2014; Zong et al, 2016). There have been many available results about continuous-time positive switched systems (Chen and Yang, 2014; Dong, 2016; Kaczorek, 2013; Liu et al, 2018a; Xiang and Xiang, 2013b, 2014; Xing et al, 2017; Zhang et al, 2016a; Zhao et al, 2012) and discrete-time positive switched systems (Fornasini and Valcher, 2012; Zhang et al, 2013; Zheng and Feng, 2015).…”

Guaranteed Cost Finite‐Time Control of Discrete‐Time Positive Impulsive Switched Systems

“…In [29], the problem of guaranteed cost finite-time control for positive switched linear systems with time-varying delays was considered and a cost function of positive systems (or positive switched systems) was also presented. Based on [29], [30] extended guaranteed cost finite-time control to positive switched nonlinear systems with -perturbation. It is worth noting that [28][29][30] are involved in continuous-time positive switched systems.…”

“…Based on [29], [30] extended guaranteed cost finite-time control to positive switched nonlinear systems with -perturbation. It is worth noting that [28][29][30] are involved in continuous-time positive switched systems. However, the problem of guaranteed 2 Complexity cost finite-time control for discrete-time positive impulsive switched systems is still open, which inspires us for this study.…”