Constrained hybrid control for parametric uncertainty systems via step-function method

Yawei Shi; Hongjuan Wu; Chuandong Li; Yawei Shi; Hongjuan Wu; Chuandong Li

doi:10.3934/mbe.2022503

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 11: 10741-10761. doi: 10.3934/mbe.2022503

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Constrained hybrid control for parametric uncertainty systems via step-function method

1.
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
2.
School of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing 404120, China

Academic Editor: Xiaodi Li

Received: 01 July 2022 Revised: 13 July 2022 Accepted: 14 July 2022 Published: 28 July 2022

In this paper, considering that sometimes signal transmission may be interrupted, or signal input errors may occur, we establish a novel class of parametric uncertainty hybrid control system models including the impulsive control signals under saturated inputs, which can reflect the signal transmission process more realistically. Based on the step-function method, improved polytopic representation approach and Schur complement, we find the stability conditions, which are less conservative than those with the traditional Lyapunov method, of the considered control system. In addition, we investigate the design of the control gains and the auxiliary control gains for easily finding the suitable control signals, the auxiliary signals and the estimation of the attraction domain. Moreover, our proposed methods are applied to the fixed time impulse problems of uncertain systems with or without Zeno behavior. Simulation results for the uncertain neural network systems are presented to show the feasibility and effectiveness of our stabilization methods using the step-function.
- parametric uncertainty,
- saturated inputs,
- step-function,
- attraction domain,
- Zeno behavior
Citation: Yawei Shi, Hongjuan Wu, Chuandong Li. Constrained hybrid control for parametric uncertainty systems via step-function method[J]. Mathematical Biosciences and Engineering, 2022, 19(11): 10741-10761. doi: 10.3934/mbe.2022503

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Abstract

In this paper, considering that sometimes signal transmission may be interrupted, or signal input errors may occur, we establish a novel class of parametric uncertainty hybrid control system models including the impulsive control signals under saturated inputs, which can reflect the signal transmission process more realistically. Based on the step-function method, improved polytopic representation approach and Schur complement, we find the stability conditions, which are less conservative than those with the traditional Lyapunov method, of the considered control system. In addition, we investigate the design of the control gains and the auxiliary control gains for easily finding the suitable control signals, the auxiliary signals and the estimation of the attraction domain. Moreover, our proposed methods are applied to the fixed time impulse problems of uncertain systems with or without Zeno behavior. Simulation results for the uncertain neural network systems are presented to show the feasibility and effectiveness of our stabilization methods using the step-function.

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