Stability analysis of descriptor systems with multiple commensurate time-delays

Zahedi, Fatemeh; Haeri, ءMohammad

doi:10.1016/j.jfranklin.2019.03.036

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…Similarly, we prove the necessity by putting (E,A) in the Weierstrass form as (18). Because the system (1) is admissible and has L 2 -gain, from w to z, being smaller than γ, there exists a matrix P 1 > 0 satisfying (26). Using this P 1 in (25), the existence of P 2 and P 3 satisfying ( 25) is obvious.…”

Section: Generalized Bounded Real Lemmamentioning

confidence: 81%

“…This illuminates that J is Hurwitz, as P 1 is positive definite. Subsequently, by (26), kC 1 (sI [32,33]); therefore, system (1) is admissible and has L 2 -gain, from w to z, smaller than γ.…”

Section: Generalized Bounded Real Lemmamentioning

confidence: 99%

“…Static constraints on physical variables and impulsive elements can be described explicitly using a descriptor form [2]. Many approaches in control theory based on the state‐space representation have been generalized for descriptor systems, such as stability, controllability, observability, optimal control, robust control, H ∞ ‐control, pole placement, eigenstructure assignment, time‐delay, and observer design (see [3–29], and the references therein). In particular, some remarkable results have been reported on the admissibility and the L 2 ‐gain stability analyses of continuous‐time descriptor systems [2–17].…”

Section: Introductionmentioning

confidence: 99%

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A new generalized bounded real lemma for continuous‐time descriptor systems

Yung

2021

Asian Journal of Control

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This paper proposes a new generalized Lyapunov theorem and a new generalized bounded real lemma for continuous‐time linear descriptor systems. First, we provide a necessary and sufficient condition in terms of strict linear matrix inequalities (LMIs) for the admissibility of descriptor systems. Subsequently, we demonstrate that a descriptor system is L2‐gain stable if and only if two strict LMIs are feasible. Other than existing results, only one matrix variable in the LMIs needs to be solved that can be indefinite. Some illustrative examples are provided to validate the theoretical results.

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Section: Generalized Bounded Real Lemmamentioning

confidence: 81%

Section: Generalized Bounded Real Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A new generalized bounded real lemma for continuous‐time descriptor systems

Yung

2021

Asian Journal of Control

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“…Descriptor systems also commonly called singular, generalized state‐space or differential‐algebraic equation systems, are widely used to describe a variety of practical systems . For instance, constrained robots, flexible‐link manipulators, aerospace applications, biological systems, mechanical systems, electrical circuits, and power systems can be modeled mathematically by descriptor systems.…”

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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