Controllability of Linear Control Systems on Lie Supergroup*

Abstract

In the study of supersymmetry, we encounter the systems whose dynamics are represented using both commuting and anticommuting variables. Thus, the state-space of those dynamical systems becomes a supermanifold. Though the dynamical systems emerging from natural phenomena are nonlinear in nature, linear control systems play a vital role in studying the systems locally. Therefore, we study the linear control system on Lie supergroups along with its controllability criterion. Moreover, we prove our results using Lie supergroups SL(m|n) and OSp(m|n) of lower dimensions.