Estimation of stability region for discrete‐time linear positive switched systems with multiple equilibrium points

Liu, Zhi; Zhang, Xianfu; Li, Haitao

doi:10.1002/asjc.2001

Cited by 5 publications

(5 citation statements)

References 28 publications

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“…Remark 3 Most results on MEPs issues adopted the proportional control [43]- [45]. The proportional control suffers from a deviation issue in steady-state.…”

Section: Volume mentioning

confidence: 99%

“…In [37]- [43], a switched system with MEPs was modeled and simulated, and the stability of the system was reflected by the system would eventually stay in a region related to the equilibrium points. In [44], [45], the system state of SPSs-MEPs without controller would be stable in a positive region, their numerical simulation systems were two-dimensional, and the stability region is a circle. In this section, two examples of liquid level control system are presented to demonstrate the validity of the primary outcomes.…”

Section: B Observer-based Pid Controlmentioning

confidence: 99%

“…For SPSs with MEPs (SPSs-MEPs), the literature [44] and [45] analyzed the regional stability by constructing some novel Lyapunov functions. Some aspects should be noted.…”

Section: Introductionmentioning

confidence: 99%

“…First, the regional stabilization of SPSs-MEPs has not been investigated. Different from the stability analysis of SPSs-MEPs [44], [45] and the control design for SPSs with common equilibrium points, the regional control design requires a novel control framework. How to construct a control framework on SPSs-MEPs is a significant but difficult topic.…”

Section: Introductionmentioning

confidence: 99%

“…There have been some results on the stability of SPSs with zero equilibrium point [13]- [18], PID control of PSs [32], [33], practical stability of switched systems with MEPs [37]- [43], and regional stability of SPSs-MEPs [44], [45]. However, the observation and regional PID control of SPSs-MEPs are still open.…”

Section: Introductionmentioning

confidence: 99%

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Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points

Zhang,

Jia

2024

IEEE Open J. Control. Syst.

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This paper investigates the regional control problem of switched positive systems with multiple equilibrium points. A proportional-integral-derivative controller is designed by combining the output, the error between the state and the equilibrium point, and the difference of output. A cone is introduced to design the final stable region. Two classes of copositive Lyapunov functions are constructed to achieve the stability and regional stability of subsystems and the whole systems, respectively. Then, a novel class of observers with multiple equilibrium points is proposed using a matrix decomposition approach. The observer-based proportional-integral-derivative control problem is thus solved and all states are driven to the designed cone region under the designed controller. All conditions are formulated in the form of linear programming. The novelties of this paper lie in that: (i) A proportional-integral-derivative control framework is introduced for the considered systems, (ii) Luenberger observer is developed for the observer with multiple equilibrium points, and (iii) Copositive Lyapunov functions and linear programming are employed for the analysis and design of controller and observer. Finally, the effectiveness of the proposed design is verified via two examples.

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“…Remark 3 Most results on MEPs issues adopted the proportional control [43]- [45]. The proportional control suffers from a deviation issue in steady-state.…”

Section: Volume mentioning

confidence: 99%

Section: B Observer-based Pid Controlmentioning

confidence: 99%

“…For SPSs with MEPs (SPSs-MEPs), the literature [44] and [45] analyzed the regional stability by constructing some novel Lyapunov functions. Some aspects should be noted.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points

Zhang,

Jia

2024

IEEE Open J. Control. Syst.

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Stability analysis of discrete‐time switched positive linear systems with unstable subsystem

Liu,

Zhang,

Karimi

et al. 2024

Asian Journal of Control

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This paper deals with the problem of stability analysis for discrete‐time switched positive linear systems with unstable subsystems. The fundamental concept involves utilizing the stability properties of switching behavior to counteract the state divergence introduced by unstable systems. Moreover, the existing results in the literature lack a method that can simultaneously address the stability analysis of switching positive systems containing only stable subsystems or containing unstable subsystems or only unstable subsystems. Therefore, in this paper, based on the widely used discretization Lyapunov function method in time‐delay systems, a new dwell‐time dependent co‐positive Lyapunov function was proposed by applying it to switched positive systems. A computable sufficient condition for stability analysis of switched linear systems with unstable subsystems was established within the dwell time framework. To verify the effectiveness of the results, this paper provides a numerical example and an example of supersaturated cross signal control for illustration, as well.

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Region stability of switched DTL systems with all subsystems unstable and multi-equilibria

Zhu

Qiu

Yan

2023

Information Sciences

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Estimation of stability region for discrete‐time linear positive switched systems with multiple equilibrium points

Cited by 5 publications

References 28 publications

Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points

Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points

Stability analysis of discrete‐time switched positive linear systems with unstable subsystem

Region stability of switched DTL systems with all subsystems unstable and multi-equilibria

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