Improved Stabilization Criteria for Sampled-Data Control Systems via a Less Conservative Looped-Functional Method

Khanh Hieu Nguyen,Sung Hyun Kim

doi:10.1109/access.2021.3132948

Khanh Hieu Nguyen, Sung Hyun Kim

Open Access

https://doi.org/10.1109/access.2021.3132948

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Abstract

Improved Stabilization Criteria for Sampled-Data Control Systems via a Less Conservative Looped-Functional Method

Highlights

In the past decade, the sampled-data control method has been widely studied and applied in many fields such as automotive control systems, embedded control systems, manufacturing machine control systems, and power grid control systems
The sampleddata control scheme can provide a criterion for obtaining the maximum allowable sampling interval required to reduce the computational load of digital controllers
Three main approaches have been proposed in the literature: (i) the input delay approach that incorporates the time delay resulting from the sampling process into the control input, (ii) the discrete-time approach that transforms the sampled-data system into a discrete-time parameter varying system, and (iii) the impulsive model approach that utilizes the impulsive modeling of sampled-data systems

Summary

INTRODUCTION

The sampled-data control method has been widely studied and applied in many fields such as automotive control systems, embedded control systems, manufacturing machine control systems, and power grid control systems (refer to [1]–[3] and references therein). Compared to [13], [17], [26], this paper proposes a refined two-sided looped functional method such that the chosen Lyapunov-Krasovskii functional can contain more input-delay-dependent state information based on the two-sided sampling interval. To achieve the less conservative stability and stabilization conditions, different from [13], [17], [26], this paper proposes two novel zero equality constraints that can strengthen the relationship between the inputdelay-dependent states and the current states through two time-varying weighting factors. To obtain a set of linear matrix inequality (LMI)-based conditions from the time derivative of the proposed Lyapunov-Krasovskii functional, a proper free-matrixbased integral inequality and a relaxation process for the time-varying weighting factors are presented in this paper. The notations 0n×m is the n × m-dimensional zero matrix, and In is the n × n-dimensional identity matrix

SYSTEM DESCRIPTION AND PRELIMINARIES

ILLUSTRATIVE EXAMPLES

CONCLUDING REMARKS