A New Lyapunov Based Robust Control for Uncertain Mechanical Systems

We design a new robust controller for uncertain mechanical systems. The inertia matrix's singularity and upper bound property are first analyzed. It is shown that the inertia matrix may be positive semi-definite due to over-simplified model. Further-more, the inertia matrix's being uniformly bounded above is also limited. A robust controller is proposed to suppress the effect of uncertainty in mechanical systems with the assumption of uniform positive definiteness and upper bound of the inertia matrix. We theoretically prove that the robust control renders uniform boundedness and uniform ultimate boundedness. The size of the ultimate boundedness ball can be made arbitrarily small by the designer. Simulation results are presented and discussed.