Event-triggered control for switched singular systems with asynchronous switching and state jumps

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SummaryThis paper considers the event‐triggered control problem of nonlinear switched singular systems (NSSSs) with incremental quadratic constraints (IQCs) via a mode‐dependent hybrid triggering strategy. First, impulsive control is introduced to reduce the effect of impulse caused by switching, and the closed‐loop system is modeled as an impulsive NSSS. Then, a novel mode‐dependent hybrid event‐triggering strategy (ETS) consisting of disturbance‐influenced ETS and Lyapunov‐function‐dependent ETS is constructed to avoid Zeno behavior and asynchronous phenomena. Based on this ETS and admissible edge‐dependent average dwell time (AED‐ADT) method, some new sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that the closed‐loop system is regular, impulse‐free, has a unique solution, and is globally uniformly asymptotically stable (GUAS) with a weighted performance. Further, Zeno behavior is excluded by calculating the minimum lower bound of inter‐event time. Finally, a numerical example and a practical application are proposed to demonstrate the validity of the results.

“…Remark In References 29,36,37, the problem of state consistency was considered at instant

t_{i}

Section: Preliminariesmentioning

confidence: 99%

“…Under the ETS in Reference 29, the state trajectories and release time are given in Figures 11 and 12, respectively. Combining Figures 10 and 12, it can be seen that the number of sampling are

34

and

32

, respectively, and the ETS used in this paper ensures that sampling must occur at the switching instant without a significant increase of sampling.…”

Section: Examplesmentioning

confidence: 99%

“…Combining Figures 10 and 12, it can be seen that the number of sampling are

34

and

32

0

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Aperiodic sampled‐data stabilization of switched singular systems with asynchronous switching: A hybrid control approach

Lin,

Wu,

Xiao

et al. 2024

This article investigates the sampled‐data stabilization problem for a class of switched singular systems with aperiodic sampling. The asynchronous switching between the plant and the switched controller caused by sampling is considered. Unlike normal systems, the conventional zero‐order hold type sampled‐data control law may be inapplicable to singular systems. This is because under that control law, the algebraic equations of singular systems may have no solutions at sampling instants. To cope with this problem, a new hybrid control law composed of a mode‐dependent impulsive controller and a mode‐dependent sampled‐data state feedback controller is devised. The impulsive controller adjusts the values of differential substate at sampling instants so that the algebraic equations are solvable. Then, by constructing a novel piecewise sampling‐time‐dependent Lyapunov function and using the average dwell time method as well as convex technique, a sampling‐range‐dependent sufficient condition for exponential stability of the resulting closed‐loop system is established. Moreover, an optimization‐based method is proposed to solve the hybrid controller gains. Simulation results on two examples including a mechanical arm system show the effectiveness of the proposed control method.

Estimation of real‐time reachable set on nonlinear time‐delay switched singular systems with state jump

Feng,

Zhang,

Liu

et al. 2024

This article addresses the real‐time reachable set problem on nonlinear time‐delay switched singular systems with state jump, which is subject to initial state and peak‐bound disturbance. Initially, based on the system state decomposition method, a state jump lemma is proposed, which combines the nonlinear function and the system state at the switching instant. Then, a real‐time bounded lemma is developed, premised on using the idea of average dwell‐time and analyzing subinterval function changes. Afterwards, the sufficient conditions for estimating the real‐time and nonreal‐time reachable set are established, which ensures that the reachable state of system can be restricted within a real‐time or nonreal‐time closed set. Finally, simulation results of the typical Direct Current boost chopper are performed to exhibit the effectiveness of the devised estimation scheme for the real‐time reachable set of system.