Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay

Cai, Xiushan; Wang, Zhenyun; Liu, Leipo

doi:10.1016/j.neucom.2015.03.008

Cited by 13 publications

(5 citation statements)

References 22 publications

(25 reference statements)

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“…Remark 2: The scheme proposed in Theorem 1 involves a robust delay range-dependent stability criterion for solving the feedback stability problem. Previous approaches offer the stability condition of the system without considering the impact of delayed terms, as proposed in [22], [23], [24], and [25]. This study involves a more generic delay-rangedependent approach with nonzero upper and lower bounds.…”

Section: Resultsmentioning

confidence: 99%

“…Delay-dependent stability schemes are utilized to overcome traditionalism in delays in reference to a delayindependent scheme. Moreover, a more specific condition involves the reflection of the delay starting from a constant lower limit (other than zero) to a definite upper limit [22], [23], [24], [25]. In [26], a delay-range-dependent scheme was studied to determine stability by considering Jensen's inequality.…”

Section: Introductionmentioning

confidence: 99%

“…2. The regional stability of the robust estimation-based control of nonlinear systems with delayed dynamics is ensured by Lyapunov retreatment with Wirtinger's inequality results and local region selection, in contrast to existing techniques [22], [23], [24], [25], [26]. Previously, Jensen's inequality was used to provide a solution of integral terms; therefore, generic treatment was a motivating aspect of the study.…”

Section: Introductionmentioning

confidence: 99%

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Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Mirza,

Ahmad,

Masood

et al. 2024

IEEE Access

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This study presents a robust estimation-based control approach for nonlinear systems with generalized one-sided Lipschitz (OSL) conditions projected for delay measurement. A control scheme was devised for this family of nonlinear systems by deploying the Lyapunov-Krasovskii (LK) method for the delayed system and by encompassing the generalized OSL inequality without using the quadratic inner boundedness (QIB) condition to overcome the conservatism introduced by the QIB condition. The stability of the resulting system is attained by employing a delay-range-dependent technique, while the derivative of the LK functional is scouted using Wirtinger's inequality, which shrinks the conservativeness of typical Jensen's inequality, resulting in stability in the form of linear matrix inequalities (LMIs). Moreover, a sufficient and necessary solution for the main results was achieved through a decoupling mechanism to acquire the controller and estimator gains simultaneously using iterative optimization tools. To attenuate the effects of external disturbances on the system, the L2 gain of the error with reference to the system was computed and incorporated into the dynamics. Furthermore, the LMI-based results are handled using the cone complementary linearization (CCL) method to authenticate the controller and observer gains via convex optimization. Finally, a numerical example demonstrates the success of the presented robust observer control formation for generalized OSL nonlinear systems in the presence of output delays.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Mirza,

Ahmad,

Masood

et al. 2024

IEEE Access

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“…In the control literature, OSL conditions have been recently applied to control and stabilization [1,7], but do not make use of Euler's method. To our knowledge, our work applies for the first time Euler's scheme with OSL conditions to the symbolic control of hybrid systems.…”

Section: Related Workmentioning

confidence: 99%

Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

Coënt

Vuyst

Chamoin

et al. 2017

Electron. Proc. Theor. Comput. Sci.

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In this paper, we propose a symbolic control synthesis method for nonlinear sampled switched systems whose vector fields are one-sided Lipschitz. The main idea is to use an approximate model obtained from the forward Euler method to build a guaranteed control. The benefit of this method is that the error introduced by symbolic modeling is bounded by choosing suitable time and space discretizations. The method is implemented in the interpreted language Octave. Several examples of the literature are performed and the results are compared with results obtained with a previous method based on the Runge-Kutta integration method.

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“…Recently, several interesting works on stabilisation for this type of system were carried out. In [23], the control synthesis conditions for OSL differential inclusion systems were provided. In [24], a novel observer‐based controller design was proposed for OSL systems.…”

Section: Introductionmentioning

confidence: 99%

Robust observer‐based finite‐time control for one‐sided Lipschitz singular systems with uncertainties

Ren

2020

IET Control Theory & Appl

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Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay

Cited by 13 publications

References 22 publications

Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

Robust observer‐based finite‐time control for one‐sided Lipschitz singular systems with uncertainties

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