## Passivity-based sliding mode control of uncertain singular time-delay systems.(English)Zbl 1175.93065

Summary: The problem of Sliding Mode Control (SMC) with passivity of a class of uncertain nonlinear singular time-delay systems is studied. An integral-type switching surface function is designed by taking the singular matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain singular time-delay system. By introducing some slack matrices, a delay-dependent sufficient condition is proposed in terms of linear matrix inequality, which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive. The passification solvability condition is then established. Moreover, a SMC law and an adaptive SMC law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

### MSC:

 93B35 Sensitivity (robustness) 93B12 Variable structure systems 93D99 Stability of control systems 93C10 Nonlinear systems in control theory 93C41 Control/observation systems with incomplete information
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### References:

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