Variable structure system

A variable structure system, or VSS, is a discontinuous nonlinear system of the form

${\dot {\mathbf {x} }}=\varphi (\mathbf {x} ,t)$

where $\mathbf {x} \triangleq [x_{1},x_{2},\ldots ,x_{n}]^{\operatorname {T} }\in \mathbb {R} ^{n}$ is the state vector, $t\in \mathbb {R}$ is the time variable, and $\varphi (\mathbf {x} ,t)\triangleq [\varphi _{1}(\mathbf {x} ,t),\varphi _{2}(\mathbf {x} ,t),\ldots ,\varphi _{n}(\mathbf {x} ,t)]^{\operatorname {T} }:\mathbb {R} ^{n+1}\mapsto \mathbb {R} ^{n}$ is a piecewise continuous function. Due to the piecewise continuity of these systems, they behave like different continuous nonlinear systems in different regions of their [[state space (controls){{}} Archived 2017-07-25 at the Wayback Machine