| Citation: |
Yanchao He, Yuzhen Bai. EXPONENTIAL STABILITY AND APPLICATIONS OF SWITCHED POSITIVE LINEAR IMPULSIVE SYSTEMS WITH TIME-VARYING DELAYS AND ALL UNSTABLE SUBSYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2369-2391. doi: 10.11948/20230392
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EXPONENTIAL STABILITY AND APPLICATIONS OF SWITCHED POSITIVE LINEAR IMPULSIVE SYSTEMS WITH TIME-VARYING DELAYS AND ALL UNSTABLE SUBSYSTEMS
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Abstract
The global uniform exponential stability of switched positive linear impulsive systems with time-varying delays and all unstable subsystems is studied in this paper, which includes two types of distributed time-varying delays and discrete time-varying delays. Switching behaviors dominating the switched systems can be either stabilizing or destabilizing in the new designed switching sequence. We design new linear programming algorithm process to find the feasible ratio of stabilizing switching behaviors, which can be compensated by unstable subsystems, destabilizing switching behaviors, and impulses. Specifically, we add a kind of nonnegative impulses which is consistent with the switching behaviors for the systems. Employing a multiple co-positive Lyapunov–Krasovskii functional, we present several new sufficient stability criteria and design new switching sequence. Then, we apply the obtained stability criteria to the exponential consensus of linear delayed multi-agent systems, and obtain the new exponential consensus criteria. Three simulations are provided to demonstrate the proposed stability criteria.
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Keywords:
- Exponential stability /
- switched systems /
- impulses /
- distributed time-varying delays
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References
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Yanchao He, Yuzhen Bai. EXPONENTIAL STABILITY AND APPLICATIONS OF SWITCHED POSITIVE LINEAR IMPULSIVE SYSTEMS WITH TIME-VARYING DELAYS AND ALL UNSTABLE SUBSYSTEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2369-2391. doi: 10.11948/20230392
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Figure 1.
The sketch map process of adjusting the original switching sequence with
$ m=4 $ $ [t_{l1}, t_{l2}] $ $ [t_{l1}, t_{{l1}+1}] $ $ [t_{{l1}+1}, t_{l2}] $ $ |M_{k}^{\uparrow}|= m_{1} $ $ |M_{k}^{\downarrow}|= m_{2} $ $ m_{1}+m_{2}=4 $ $ m_{1}=1 $ $ m_{2}=3 $ -
Figure 2.
The influence factors of GUES for SPLISs (1.1) and (1.2).
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Figure 3.
The state trajectories of three subsystems of SPLISs (1.1).
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Figure 4.
The signals and state trajectories of SPLISs (1.1).
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Figure 5.
The state trajectories of three subsystems of SPLISs (1.2).
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Figure 6.
The signals and state trajectories of SPLISs (1.2).
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Figure 7.
The state trajectories of two subsystems of systems (4.1).
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Figure 8.
The signals and state trajectories of systems (4.1).