Research Papers

Global Sliding Mode Control Via Linear Matrix Inequality Approach for Uncertain Chaotic Systems With Input Nonlinearities and Multiple Delays

[+] Author and Article Information
Mona Afshari, Rahman Hajmohammadi

Electrical Engineering Department,
University of Zanjan,
Zanjan 45371-38791, Iran

Saleh Mobayen

Electrical Engineering Department,
University of Zanjan,
P.O. Box 38791-45371,
Zanjan 45371-38791, Iran
e-mail: mobayen@znu.ac.ir

Dumitru Baleanu

Department of Mathematics and
Computer Sciences,
Faculty of Arts and Sciences,
Çankaya University,
Ankara 06530, Turkey;
Institute of Space Sciences,
Magurele-Bucharest 77125, Romania

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 23, 2017; final manuscript received November 22, 2017; published online January 12, 2018. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 13(3), 031008 (Jan 12, 2018) (14 pages) Paper No: CND-17-1041; doi: 10.1115/1.4038641 History: Received January 23, 2017; Revised November 22, 2017

This paper considers a global sliding mode control (GSMC) approach for the stabilization of uncertain chaotic systems with multiple delays and input nonlinearities. By designing the global sliding mode surface, the offered scheme eliminates reaching phase problem. The offered control law is formulated based on state estimation, Lyapunov–Krasovskii stability theory, and linear matrix inequality (LMI) technique which present the asymptotic stability conditions. Moreover, the proposed design approach guarantees the robustness against multiple delays, nonlinear inputs, nonlinear functions, external disturbances, and parametric uncertainties. Simulation results for the presented controller demonstrate the efficiency and feasibility of the suggested procedure.

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Grahic Jump Location
Fig. 2

State estimation errors

Grahic Jump Location
Fig. 3

Output estimation error ey(t)

Grahic Jump Location
Fig. 4

Applied control signal

Grahic Jump Location
Fig. 1

The continuous function tanh(.) with different values of steepness

Grahic Jump Location
Fig. 5

The responses of the estimation errors

Grahic Jump Location
Fig. 6

Time history of the output estimation error

Grahic Jump Location
Fig. 7

Applied control input



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