Exponential Stability Analysis for Discrete-Time Singular Systems with Randomly Occurring Delay

Li, Zuxin; Su, Hongye; Gu, Yong; Wu, Zheng‐Guang

doi:10.1007/s00034-013-9561-z

Cited by 5 publications

(3 citation statements)

References 29 publications

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“…Hence, this class of systems along with the field of singularities have attracted a great deal of interest in the control system's research community . Causality, regulation, and stabilization are a vital topics in the study of discrete‐time descriptor systems . Time delays are quite common in practical applications and have an impact on system's causality, regulation, and stability .…”

Section: Introductionmentioning

confidence: 99%

Robust global controller design for discrete‐time descriptor systems with multiple time‐varying delays

Mobayen

Bayat

Omidvar

et al. 2020

Intl J Robust & Nonlinear

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Descriptor systems are ubiquitous in many complex practical systems including spacecraft, electrical networks, economic systems, robotic, vibrational, and structural systems. Time delays are ubiquitous in those complex systems. If not addressed properly at the control design stage, they will result in singularities such as oscillation, instability, degraded performance. This article proposes a novel linear matrix inequality (LMI)-based global sliding mode control (GSMC) approach for uncertain discrete-time descriptor systems with multiple time-varying delays. Strict LMI conditions are established based on free-weighting matrices and the Lyapunov-Krasovskii functional to guarantee admissible closed-loop dynamics, that is, regular, causal, and stable. The sufficient condition for the asymptotic stability of the sliding mode dynamics is obtained based on the Lyapunov stability theorem and LMI constraint. The GSMC approach is then formulated based on a global sliding surface to ensure robust performance of the closed-loop system against parametric uncertainties and time delays, while eliminating the reaching phase. The global sliding surface ensures robust performance without the need for a reaching phase, thus establishing sliding around the surface right from the beginning and reducing the control effort. The effectiveness and validity of the proposed approach is assessed using a numerical example. K E Y W O R D Sdiscrete-time descriptor systems, global sliding mode control, LMI, multiple time-varying delay, parametric uncertainties

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Section: Introductionmentioning

confidence: 99%

Robust global controller design for discrete‐time descriptor systems with multiple time‐varying delays

Mobayen

Bayat

Omidvar

et al. 2020

Intl J Robust & Nonlinear

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show abstract

“…It is worth noticing that the robust stability problem for singular systems is much more complicated than that for regular systems because it requires considering not only stability robustness, but also regularity and absence of impulses (for continuous singular systems) and causality (for discretesingular systems) at the same time, and the latter two need not be considered in regular systems. There are lots of papers that have studied these subjects [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we address the problems of robust stability and stabilization for uncertain singular systems with randomly occurring time-varying delay (ROTD). Although the randomly occurring delay has appeared in some papers [1,10,11], few related results have been established for uncertain singular systems.…”

Section: Introductionmentioning

confidence: 99%

Reliable Control for Uncertain Singular Systems with Randomly Occurring Time-Varying Delay and Actuator Faults

Yu-lin

Zhao

et al. 2015

Abstract and Applied Analysis

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The problem of reliable control is investigated for uncertain continuous singular systems with randomly occurring time-varying delay and actuator faults in this work. The delay occurs in a random way, and such randomly occurring delay obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. The uncertainties under consideration are norm-bounded, and may vary with time. Then, with the constructed Lyapunov function, a sufficient condition is given to ensure the unforced system is mean-square exponentially stable and the corresponding controller can be derived from such condition, and the actuator faults problem is guaranteed. A numerical example is provided to show the effectiveness of the methods.

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Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances

2017

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Exponential Stability Analysis for Discrete-Time Singular Systems with Randomly Occurring Delay

Cited by 5 publications

References 29 publications

Robust global controller design for discrete‐time descriptor systems with multiple time‐varying delays

Robust global controller design for discrete‐time descriptor systems with multiple time‐varying delays

Reliable Control for Uncertain Singular Systems with Randomly Occurring Time-Varying Delay and Actuator Faults

Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances

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