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**Reduced-order design of high-order sliding mode control system.**
*(English)*
Zbl 1237.93037

Summary: To design an \(r\)-th \((r>2)\) order sliding mode control system, a sliding variable and its derivatives of up to (\(r - 1\)) are in general required for the control implementation. This paper proposes a reduced-order design algorithm using only the sliding variable and its derivatives of up to (\(r - 2\)) as the extension of the second-order asymptotic sliding mode control. For a linear time-invariant continuous-time system with disturbances, it is found that a high-order sliding mode can be reached locally and asymptotically by a reduced-order sliding mode control law if the sum of the system poles is less than the sum of the system zeros. The robust stability of the reduced-order high-order sliding mode control system, including the convergence to the high-order sliding mode and the convergence to the origin is proved by two Lyapunov functions. Simulation results show the effectiveness of the proposed control algorithm.

### MSC:

93B12 | Variable structure systems |

93B11 | System structure simplification |

93C15 | Control/observation systems governed by ordinary differential equations |

### Keywords:

variable structure control; high-order sliding mode control; reduced-order control; asymptotic stability; Lyapunov function
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\textit{Y. Pan} et al., Int. J. Robust Nonlinear Control 21, No. 18, 2064--2078 (2011; Zbl 1237.93037)

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