Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

This study proposes a novel variable structure control (VSC) for the mismatched uncertain systems with unknown time-varying delay. The novel VSC includes the finite-time convergence sliding mode, invariance property, asymptotic stability, and measured output only. A necessary and sufficient condition guaranteeing the existence of sliding surface is given. A novel lemma is established to deal with the control design problem for a wider class of time-delay systems. A suitable reduced-order observer (ROO) is constructed to estimate unmeasured state variables of the systems. A novel finite-time output feedback controller (FTOFC) is investigated, which is based on the ROO tool and the Moore-Penrose inverse technique. Moreover, with the help of this lemma and the proposed FTOFC, restrictions on most existing works are also eliminated. In addition, an asymptotic stability analysis is implemented by means of the feasibility of the linear matrix inequalities (LMIs) and given desirable sliding mode dynamics. Finally, a MATLAB simulation result on a numerical example is performed to show the effectiveness and advantage of the proposed method.

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“…So, we can easily select matrix such that the matrix is semipositive definite. Then, from Lemma 3 of [35], the following is true:…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Shift exp(− max ) to the right-hand side term of inequality (49) and use the Lemma 3 of [35]; that is, ‖ ( − ( ))‖ ≤…”

Section: Theorem 18 Let Error (0) Be An Initial Condition Of the Errmentioning

confidence: 99%

Finite‐Time Output Feedback Controller Based on Observer for the Time‐Varying Delayed Systems: A Moore‐Penrose Inverse Approach

Nguyen

Tsai

2017

Mathematical Problems in Engineering

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“…Substituting system (2) into the derivative of s(t) with respect to time can obtain [28], define two regions Ω 1 and Ω 2 as…”

Section: Integral Sliding Surface and Sliding Mode Controllermentioning

confidence: 99%

“…When the system states are partly obtainable, both state observers [10][11][12][13][14] and output feedback controllers [15][16][17][18][19][20][21] are feasible schemes to stabilize time-delay systems. In the field of state observers, Darouach [14] has developed an observer methodology to estimate states of linear time-delay systems with noises and mismatched disturbances.…”

Section: Introductionmentioning

confidence: 99%

“…Niu et al [16] extended an observer-based sliding mode control using the LMI technique to regulate uncertain time-delay systems. Yan et al [19] applied an effective slidingmode design technique using outputs only to control the time-delay systems with disturbances. Pai [21] proposed a Luenberger observer-based output feedback controller for a class of nonlinear uncertain state-delay systems with matched uncertainties and disturbances.…”

Section: Introductionmentioning

confidence: 99%

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Applying output feedback integral sliding mode controller to uncertain time-delay systems with mismatched disturbances

Ting

Chang

Chen

2011

Int. J. Control Autom. Syst.

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For time-delay systems with mismatched disturbances and uncertainties, this paper develops an integral sliding mode control algorithm using output information only to stabilize the systems. An integral sliding surface is comprised of output signals and an auxiliary full-order compensator. The proposed output feedback sliding mode controller can satisfy the reaching and sliding condition and maintain the system on the sliding surface from the initial moment. When two specific algebraic Riccati inequalities have solutions, our method can guarantee the stability of the closed-loop system and satisfy the property of robust disturbance attenuation. Moreover, the design parameters of controller and compensator can be simultaneously determined by solutions to the algebraic Riccati inequalities. Finally, two numerical examples illustrate the applicability of the proposed scheme.

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References

2014

Sliding Mode Control of Uncertain Parameter‐Switching Hybrid Systems

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Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

Cited by 56 publications

References 25 publications

Finite‐Time Output Feedback Controller Based on Observer for the Time‐Varying Delayed Systems: A Moore‐Penrose Inverse Approach

Finite‐Time Output Feedback Controller Based on Observer for the Time‐Varying Delayed Systems: A Moore‐Penrose Inverse Approach

Applying output feedback integral sliding mode controller to uncertain time-delay systems with mismatched disturbances

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