Generalized average dwell time approach to stability and input-to-state stability of hybrid impulsive stochastic differential systems

Yao, Fengqi; Cao, Jinde; Cheng, Pei; Li, Qiu

doi:10.1016/j.nahs.2016.04.002

Cited by 38 publications

(25 citation statements)

References 34 publications

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“…transform the ith subsystem into the form of (6) and obtain the matrix R i (x); iv. obtain condition (10) with P i , K i (x, k m ), R i (x); v. according to (10) and (13), solve out the interval value of k m with the SP algorithm described in Section 3.3; vi. repeat the aforementioned steps to solve out the interval value of k m for each subsystem belongs to M p ; vii.…”

Section: Robust H ∞ Control: Parameterization Of Controller Approachmentioning

confidence: 99%

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Zhu

Hou

2018

Intl J Robust & Nonlinear

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Summary This paper considers the global feedback exponential stabilization and L2 gain disturbance attenuation problems of the switched nonlinear polynomial systems with passive and nonpassive subsystems for any given average dwell time. In the existing result, it needs that there exists at least one open loop passive subsystem in the switched nonlinear system, which is unnecessary for the switched nonlinear polynomial system in this paper because the passivity of the subsystem can be obtained according to the passivity‐based feedback dissipative Hamiltonian realization. In addition, a parameterization of controller approach–based feedback exponential stabilization method of nonlinear polynomial system is described and utilized such that the Lyapunov function of the passive subsystem possesses the required decay rate to exponentially stabilize the switched nonlinear polynomial system. Comparing with the controller designed with the existing method, the obtained controller in this paper has much simpler structure and better performance. An example simulation is provided to illustrate the effectiveness of the proposed approach.

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Section: Robust H ∞ Control: Parameterization Of Controller Approachmentioning

confidence: 99%

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Zhu

Hou

2018

Intl J Robust & Nonlinear

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“…ISS property analysis of nonlinear systems with disturbance inputs is one of active research topics in modern nonlinear control theory. Therefore, it is of great significance to study ISS for impulsive systems, see, eg, other works …”

Section: Introductionmentioning

confidence: 99%

“…Most of the existing results pertain to the study of ISS property for continuous‐time impulsive systems, see other works and the references therein, but fewer studies the ISS property for discrete‐time impulsive systems . In addition, time delays occur frequently in many real‐world phenomena.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, many systems in the real world may be disturbed by stochastic factors. In the past decades, there has been an increasing interest in the ISS property analysis of continuous‐time stochastic impulsive systems, see other works and the references therein. In the work of Wu et al, by means of the Lyapunov‐Krasovskii functional and the average impulsive interval approach, the ISS, integral‐ISS, and stochastic‐ISS for continuous‐time impulsive stochastic delayed systems are considered under linear assumptions.…”

Section: Introductionmentioning

confidence: 99%

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pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

2018

Intl J Robust & Nonlinear

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Summary This paper investigates the pth moment exponential input‐to‐state stability (ISS) of nonlinear discrete‐time impulsive stochastic delay systems. By employing Lyapunov functionals, some pth moment exponential ISS criteria are provided. The obtained results show that a discrete‐time stochastic delay system can become pth moment exponential input‐to‐state stable by impulsive controls even if it may be not input‐to‐state stable itself. On the other hand, the original system without impulses can retain its ISS property with appropriate destabilizing impulses. As an application, the theoretical results are used to test the ISS for a class of recurrent neural networks under stochastic perturbations. Finally, a numerical example is presented to illustrate the effectiveness of the results.

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“…However, [1][2][3][4][5][6][7][8] ignore the stochastic disturbance. It is generally known that stochastic disturbance is a troublesome source which could lead to the instability of control systems, and it exists in most practical systems [9][10][11][12][13][14], especially in aerospace systems, industrial control of power systems, dynamics of epidemic diseases [15,16], and linear quadratic optimal control [17][18][19][20]. Therefore, adaptive control for stochastic nonlinear systems has received considerable attention [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Direct Adaptive Fuzzy Backstepping Control for Stochastic Nonlinear SISO Systems with Unmodeled Dynamics

Zhang

Liu

2017

Asian Journal of Control

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This paper discusses the input‐to‐state practical stability (ISpS) problem for a class of stochastic strict‐feedback systems which possess dynamic disturbances, unstructured uncertainties and unmodeled dynamics. The uncertain terms not only depend on the measurable output, but also are related with other unmeasurable states of the system. In the backstepping design, we use fuzzy logic systems directly to approach unknown control signals rather than unknown functions. A main advantage of the direct control method is that for an nth order strict‐feedback stochastic system, only four online parameters are needed. Moreover, it is proved that the closed‐loop system is ISpS in probability by using a stochastic small‐gain approach. Two simulation examples illustrate the effectiveness of the proposed scheme.

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Generalized average dwell time approach to stability and input-to-state stability of hybrid impulsive stochastic differential systems

Cited by 38 publications

References 34 publications

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

Direct Adaptive Fuzzy Backstepping Control for Stochastic Nonlinear SISO Systems with Unmodeled Dynamics

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Generalized average dwell time approach to stability and input-to-state stability of hybrid impulsive stochastic differential systems

Cited by 38 publications

References 34 publications

Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Robust H∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

pth moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

Direct Adaptive Fuzzy Backstepping Control for Stochastic Nonlinear SISO Systems with Unmodeled Dynamics

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Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach

Robust H_∞ control for uncertain switched nonlinear polynomial systems: Parameterization of controller approach