Delay-range-dependent robust BIBO stabilization of 2D discrete delayed systems via LMI approach

Wang, Limin; Chen, Xi; Gao, Furong

doi:10.3182/20140824-6-za-1003.01484

Cited by 4 publications

(5 citation statements)

References 14 publications

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“…This requires slight changes in the classical definitions of BIBO stability. Motivated by the definition of BIBO stability presented and studied in References 2,14, we introduce the next definition.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…The analysis of bounded input bounded output (BIBO) stability of systems is very important for its possible application in many aspects such as single/double‐loop modulators, or issues connected with bilinear input/output maps, and so forth. The BIBO stability for 2D discrete delayed systems is studied in Reference 14, for networked control systems with short time‐varying delays in Reference 15, for retarded systems in Reference 16, for switched uncertain neutral systems with constant delay is considered in Reference 17, for perturbed interconnected power systems in Reference 18, for feedback control system with time delays, 2 and for Lurie system with time‐varying delay in Reference 19. Recently, input‐to‐state stability was extended to Caputo fractional models in Reference 20, robust stability to uncertain multiorder fractional systems in Reference 21 and BIBO stability to fractional‐order controlled nonlinear systems in References 22,23.…”

Section: Introductionmentioning

confidence: 99%

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Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

Almeida

Hristova

2020

Intl J Robust & Nonlinear

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The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time-varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.

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Section: Statement Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

Almeida

Hristova

2020

Intl J Robust & Nonlinear

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“…Therefore, it is important to study the delay-range-dependent problem. Some results on 2D systems have appeared up to now [1,3,[21][22][23][24].…”

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confidence: 99%

“…Illustration. This section applies the main results on H ∞ control to a class of systems described by (24), as shown in [27], which exists in the thermal processes in chemical reactors, heat exchangers and pipe furnaces. Here, the time-delay is a state delay varying in an interval, which implies that the system current information is related not only to the current time information but also to the previous moments.…”

mentioning

confidence: 99%

Delay-range dependent $H_\infty$ control for uncertain 2D-delayed systems

Wang¹,

Yu²,

Shi³

et al. 2015

Numerical Algebra, Control &Amp; Optimization

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This paper proposes a delay-range dependent method to solve a two-dimensional (2D) stabilization and H∞ control problem for a class of uncertain delayed systems described by the Roessor model with a range delay. By using a new 2D Lyapunov-Krasovskii function and introducing a differential inequality to the difference Lyapunov functional for 2D systems, sufficient delay-range dependent conditions for the existence of the proposed feedback controller scheme are established in terms of linear matrix inequalities (LMIs), which depend on both the difference between the upper and lower delay bounds and the upper delay bound of the interval time-varying delay. By solving these LMIs, the 2D law is explicitly formulated, together with an adjustable robust H∞ performance level. The analysis of the application in the thermal process demonstrates the effectiveness of the proposed controller.

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“…For instance, [17] studied the BIBO stability of 2D discrete delayed systems, [18] researched the BIBO stability of fractional systems, [19] investigated study the BIBO stability of switched uncertain neutral systems, [20] concerned the BIBO stability of perturbed interconnected power systems, and [21] focused on the BIBO stability of feedback control systems. However, the results on BIBO stability for the Lurie system is seldom found at present.…”

Section: Introductionmentioning

confidence: 99%