Variable structure system
A variable structure system, or VSS, is a discontinuous nonlinear system of the form
where ![\mathbf {x} \triangleq [x_{1},x_{2},\ldots ,x_{n}]^{\operatorname {T} }\in \mathbb {R} ^{n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f92c638f65515b1a41f5b16a3392ca0bd3e3db82)
![\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}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69f94359ce57d64662bf6f5bc7b03d2b4877f534)
The development of variable structure control depends upon methods of analyzing variable structure systems, which are special cases of hybrid dynamical systems.
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