Mathematical model of a human leg: The switched linear system approach

This article presents a novel approach to modelling of the human leg with the use of linear switched systems. Second order differential equations forming a two-segments leg model moving in a vertical plane are shown. State space linear equations describing given model are derived. A linear switched system for such model is presented, where the switching function is modelled as state-dependent. Based on this approach a linear system is presented, which is composed of four subsystems between which switching occurs depending on two state variables. These variables represent angular displacements. As a consequence, a state space division is shown together with a linear system describing human leg in this setting. Finally, a set of simulations presents differences between standard linear modelling approach and a switched linear system approach.