Estimation of stability domain of mismatched uncertain variable Structure system with bounded controller

The multivariable linear system with uncertainty factors, such as uncertainty of parameters, inputs and disturbances, is considered. When control is bounded, variable structure control system may be local asymptotic stable because control law of design couldn't necessarily be implemented according to the existence condition of slide mode, so it is essential to research stability domain problem of variable structure control system. Attractive domain of sliding mode was analyzed and stability domain estimation method of sliding mode was studied by Lyapunov stability criteria, then stability of whole closed-loop system may be estimated. Effects of mismatched factor and control bound on stability domain and relation between control bound and robustness were studied. The results have indicated that introduction of various mismatched uncertain factors will reduce the range of stability domain when control bound is definite and it is necessary to enlarge control gain to extend stability domain under the same uncertain factors.