On a exponential linear model matching for a two degree of freedom manipulator

We propose a linear implicit control law for an elemental closed kinematic chain, the aim of which is to match a linear model, in an exponential way. Given any initial condition we find a sufficiently small parameter ε such that the goal is exponentially achieved for fix parameters k₀, k₁ and β. Theorem 2 states that, when the initial conditions are closed to the equilibrium point, the tracking error, between the states of the closed loop system and the desired trajectory is bounded by an exponential decreasing function. Another way to see Theorem 2 is that given any finite initial condition and some fix parameters we can find a parameter such that the error is bounded by an exponential decreasing function as the parameter tends to zero. When the closed loop system gets to the equilibrium point then error is equal to zero