## Variable structure and Lyapunov controlThis book covers a wide range of up-to-date sliding mode Variable Structure Control (VSC) and Lyapunov Control research and design techniques for the robust control of uncertain systems. In direct contrast to most adaptive controllers, these deterministic controllers employ fixed nonlinear feedback control functions, which operate effectively over a specified magnitude range of system parameter variations and disturbances. There are 18 chapters covering and discussing such topics as the theoretical and practical design of controllers for uncertain multivariable systems, novel algebraic approaches for sliding mode control, discrete-time control, and the stabilizing VSC of uncertain infinite-dimensional systems. The main areas of application include electric motor drives, robotics, flight control and space systems, as well as power electronics and chemical processes, some of which are described in the book. |

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### Contents

An Algebraic Approach to Sliding Mode Control | 23 |

Robust Tracking with a Sliding Mode | 51 |

Sliding Surface Design in the Frequency Domain | 75 |

Copyright | |

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### Common terms and phrases

adaptive control algorithm approach asymptotically stable Automatic Control boundedness chattering closed-loop Consider continuous-time control design control input control law control structure control systems convergence Corless defined denotes differential algebraic differential equation differential field discontinuous control dynamical systems eigenvalues equivalent control estimate example exists feedback control feedforward filter finite Fliess frequency hyperplane hyperrectangle ideal sliding IEEE IEEE Transactions Journal of Control Leitmann levitation linear control linear systems Lyapunov equation Lyapunov exponent Lyapunov function matching conditions matrix minimum phase module motion nonlinear control nonlinear systems observer obtained output parameters plant polynomial polytope positive definite Proc quadratic stability Riccati equation robot satisfies scalar signal Sira-Ramirez sliding manifold sliding mode control sliding surface smooth solution space stabilizable switching hyperplane symmetric matrix Theorem torque tracking error trajectory Transactions on Automatic uncertain systems uncertainty Utkin values variable structure control vector field zero Zinober