Constructive eigenvalue analysis based velocity observer design for mechanical systems

This paper presents a novel and constructive solution for the velocity estimation of a large class of mechanical systems. By employing the technical results in non-smooth analysis, a specific eigenvalue analysis problem that can be systematically solved through structured computational procedures is formulated, and the resulting globally exponentially convergent observer can therefore be generated automatically for any appropriate model input with arbitrarily complex configurations. The proposed method applies directly to non-holonomic systems with Pfaffian constraints, and its structural simplification can be further achieved for systems with uniformly bounded inertia matrix. The established results provide a major breakthrough on both the dimension and practical realizability of the prevailing Immersion & Invariance velocity observer designs, and its effectiveness is verified with numerical simulations of several representative examples.