H ∞ filtering for singular bilinear systems with application to a single-link flexible-joint robot

Zerrougui, Mohamed; Darouach, Mohamed; Boutat‐Baddas, Latifa; Ali, Harouna Souley

doi:10.1007/s12555-013-0117-6

Cited by 20 publications

(14 citation statements)

References 22 publications

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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. 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 .…”

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

View full text Add to dashboard Cite

show abstract

“…The theoretical developments for a singular system are worthwhile and there are more challenges, because the essential consideration for a singular system is admissibility which includes stability, regularity and causality for a discrete-time system (or impulse elimination for a continuous-time system). Consequently, over past decades, many different practical systems and research areas (1)(2)(3)(4)(5) have been adopted the singular system description. Many fundamentals and advanced results for a normal state-space system have been successfully extended to a singular system, such as controllability and observability (6) , (robust) stability analysis and (robust) stabilization (7)(8)(9) , H∞ control and filtering (10)(11)(12) and so forth.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, over past decades, many different practical systems and research areas (1)(2)(3)(4)(5) have been adopted the singular system description. Many fundamentals and advanced results for a normal state-space system have been successfully extended to a singular system, such as controllability and observability (6) , (robust) stability analysis and (robust) stabilization (7)(8)(9) , H∞ control and filtering (10)(11)(12) and so forth. In addition, in order to get less conservative results, singular system based methods have been adopted to study state-space systems (13,14) .…”

Section: Introductionmentioning

confidence: 99%

An Observer-Based Controller Design for a Markovian Jumping Singular System with Polytopic Uncertainties

Lee

Huang

Kung

2017

The Proceedings of the 5th International Conference on Industrial Application Engineering 2017

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In this paper, an observer-based controller design problem for a discrete-time Markovian jumping singular system (DMJSS) with polytopic uncertainties is considered, which is based on a set of necessary and sufficient conditions in terms of linear matrix inequalities (LMIs) for an admissibility analysis problem. A proposed mode dependent observer and a controller can be designed separately via two sets of derived LMI-based synthesis conditions. There are two principal contributions in this paper. One is that a set of strictly LMI-based necessary and sufficient conditions for the admissibility analysis problem for a DMJSS is extended to the case with uncertainties. Another one is that a suitable observer and a controller can be designed independently via two sets of strictly LMI-based synthesis conditions instead of a set of complex algorithm in terms of bilinear or nonconvex inequalities.

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“…T THE observer design is one of the most important research issues and has been expanded by many studies [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], such as observer-based control [14], [15], filter design [16], [17] and fault detection [18], [19]. The previous observers were designed by guaranteeing the convergence of the estimation error.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Sampled-Data Fuzzy Observer Design for Nonlinear Interconnected Systems

Koo

Park

Joo

2016

IEEE Trans. Fuzzy Syst.

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This paper presents the decentralized sampled-data fuzzy observer design techniques for nonlinear interconnected systems, which are assumed to be composed of fuzzy subsystems and unknown interconnections. To design the decentralized fuzzy observer, the estimation error dynamics is obtained and the performance function is defined. Based on the estimation error dynamics and the performance function, the continuous-time decentralized fuzzy observer is firstly proposed to minimize the interconnection bound to attenuation degree ratio (IAR). Also, the decentralized sampled-data fuzzy observers are designed by using the approximate discretization and the exact discrete-time design approaches, respectively. Each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities (LMIs). Finally, several simulation examples show the validity and superiority of proposed observer design techniques by comparing with the conventional techniques.Index Terms-Decentralized sampled-data fuzzy observer, nonlinear interconnected systems, interconnection bound to attenuation degree ratio, approximate discretization, exact discrete-time design.1063-6706 (c)

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H ∞ filtering for singular bilinear systems with application to a single-link flexible-joint robot

Cited by 20 publications

References 22 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

An Observer-Based Controller Design for a Markovian Jumping Singular System with Polytopic Uncertainties

Decentralized Sampled-Data Fuzzy Observer Design for Nonlinear Interconnected Systems

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