A sliding sector is defined as a subset of the state space, insidewhich some norm of state decreases with zero control input. In thepaper, an invariant sliding sector is defined to be such a kind ofsliding sector that with some control laws, the norm still keepsdecreasing inside the sector and the sector is an invariant subset,i.e., the state will not move out of the sector if the initial state isinside it or after the state is moved into it by some control law.Design algorithms of the invariant sliding sector and the correspondingvariable structure (VS) controller are given. The proposed VS controllerwith the invariant sliding sector ensures that the state moves from theoutside to the inside of the sector in a finite time and stays inside itforever after being moved into it, and especially ensures that the normof state keeps decreasing in the state space with a smooth VS controllaw. The resulted VS control system is quadratic stable. The simulationresult shows that the proposed VS controller has good controlperformance without chattering
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