Stability and guaranteed cost analysis of switched positive systems with mode‐dependent dwell time and sampling

Wang, Peng; Zhao, Jun

doi:10.1049/iet-cta.2019.0466

Cited by 11 publications

(14 citation statements)

References 41 publications

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“…Therefore, while designing the controller for an uncertain system, it is desirable to ensure not only the stability of the system but also a satisfactory level of performance. The problem of guaranteed cost (GC) control was addressed by Chang and Peng (1972) and has witnessed a rise in interest during the past few decades (Arshad et al, 2016; Belhaouane et al, 2019; Cao et al, 2017; Chang et al, 2020; Chen and He, 2016; Du et al, 2014; Fernando et al, 2013; Gao et al, 2012; Geromel et al, 1993; Han et al, 2014; Liu et al, 2013; Ma and Yan, 2016; Niamsup et al, 2013; Peng et al, 2007; Petersen et al 1998; Qiu et al, 2016; Rodríguez-Guerrero et al, 2019; Shi et al, 2003; Wang and Li, 2020; Wang and Liu, 2018; Wang and Zhao, 2019; Wang et al, 2019; Wu et al, 2017; Yu, 2005; Yu and Gao, 2002; Zhang et al, 2019; Zhu et al, 2019; Zuo at al., 2008). The objective of the GC control technique is to design a controller such that the closed-loop system is asymptotically stable while the closed-loop cost function is lower than a specified upper bound.…”

Section: Introductionmentioning

confidence: 99%

“…The objective of the GC control technique is to design a controller such that the closed-loop system is asymptotically stable while the closed-loop cost function is lower than a specified upper bound. The GC control strategy has been successfully implemented in a variety of real-world scenarios (Belhaouane et al, 2019; Chang et al, 2020; Dhawan and Kar, 2010, 2011; Du et al, 2014; Han et al, 2014; Liu et al, 2013; Qiu et al, 2016; Rodríguez-Guerrero et al, 2019; Wang and Li, 2020; Wang and Liu, 2018; Wang and Zhao, 2019; Wang et al, 2019; Wu et al, 2017; Zhu et al, 2018; Zhu et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

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Guaranteed cost controller for discrete time-delayed systems with actuator saturation

Srivastava

Negi

Kar

2021

Transactions of the Institute of Measurement and Control

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The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Guaranteed cost controller for discrete time-delayed systems with actuator saturation

Srivastava

Negi

Kar

2021

Transactions of the Institute of Measurement and Control

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“…In References 30‐32, the GC performance was attained by the dwell time approach with the assumption on the performance assured by subsystems 33‐36 . relaxed this assumption in References 30‐32 and realized the GC performance by the method of constructing the state‐dependent switching law, whereas, the switching instantaneous performance is not considered. What is necessary to be noticed is that bad instantaneous behaviors are likely to destruct the expected robust GC performance.…”

Section: Introductionmentioning

confidence: 99%

“…(iii) A condition is reached to render the robust GC performance and the rate anti‐bump switching performance of the SSs. Even if just the robust GC performance is driven, this condition is still more practical than that in References 30‐32 in which all subsystems must have the GC performance.…”

Section: Introductionmentioning

confidence: 99%

Robust guaranteed cost rate anti‐bump switching control for switched systems

Zhao

Pang

et al. 2021

Intl J Robust & Nonlinear

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A multi‐objective switching control strategy is presented in this paper to capture both the robust guaranteed cost (GC) performance and the rate anti‐bump switching performance of switched systems (SSs). The rate anti‐bump switching performance refers to the alleviation of big instantaneous jumps in the switched system rate. Through co‐construct of a switching law and a switching controller, the multi‐objective switching control scheme is attained. A condition is builded to capture the robust GC performance and the rate anti‐bump switching performance, conquering the possible conflict in both performance demands. Moreover, this condition claims that subsystems can capture none of the robust GC performance and the rate anti‐bump switching performance. A verification on the efficiency of the formed multi‐objective switching control approach is provided by regulating the acceleration of a switched engine model.

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“…35 Sampled-data switching policy is devised to investigate the stability of switched positive systems. 36 However, the studies on sampled positive systems mentioned above do not take account of the positivity preservation in the sampling interval. In this paper, the intersample behavior of a sampled positive system, which can be regarded as a simple hybrid positive system, will be considered for the first time.…”

Section: Introductionmentioning

confidence: 99%

On the positive stabilizability of sampled positive systems

Guo

Zhang

Chen

et al. 2021

Intl J Robust & Nonlinear

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This paper investigates the problem of positive stabilizability of single-input LTI positive systems. Firstly, for a single-input continuous-time positive linear system, it has been derived that a necessary condition of the existence of a stablilizing linear time-invariant controller is the number of nonnegative real poles not being greater than one. Inspired by that, the continuous-time positive stabilizability of systems with unstable complex poles is studied in this paper, where the third-order and higher-order cases are considered. Secondly, an enhanced method to construct the static state-feedback gain of a sampled positive system is presented, which takes account of the positivity preservation in the sampling interval. According to the method, the positive stabilizablity of the single-input second-order sampled positive system is analyzed. Some numerical examples are finally presented to illustrate the theoretical results.

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Stability and guaranteed cost analysis of switched positive systems with mode‐dependent dwell time and sampling

Cited by 11 publications

References 41 publications

Guaranteed cost controller for discrete time-delayed systems with actuator saturation

Guaranteed cost controller for discrete time-delayed systems with actuator saturation

Robust guaranteed cost rate anti‐bump switching control for switched systems

On the positive stabilizability of sampled positive systems

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