This paper tackles linear symmetries of control systems. Precisely, the symmetry of affine nonlinear systems under the action of a sub-group of general linear group GL?n;R?: First of all, the structure of state space (briefly, ss) symmetry group and its Lie algebra for a given system is investigated. Secondly, the structure of systems, which are ss-symmetric under rotations, is revealed. Thirdly, a complete classification of ss-symmetric planar systems is presented. It is shown that for planar systems there are only four classes of systems which are ss-symmetric with respect to four linear groups. Fourthly, a set of algebraic equations are presented, whose solutions provide the Lie algebra of the largest connected ss-symmetry group. Finally, some controllability properties of systems with ss-symmetry group are studied. As an auxiliary tool for computation, the concept and some properties of semi-tensor product of matrices are included. Copyright

In this paper, terminal sliding mode control design is considered. A control method, different from many existing terminal sliding model control design methods, is proposed based on a new switching law and continuous finite-time control ideas. Then terminal sliding mode control laws are constructed for some classes of nonlinear systems.