State-space for non-linear algebraically constrained dynamical systems

Abstract

Non-linear state differential equations x = f(x, u) with algebraic constraints g(x, u, e) = 0, e = e (t), which describe possibly singular systems, are considered. The derivation of equivalent unconstrained state differential equations x* = f* (x*, e, ė,...), {x* }c:{x} ≥ {x} with the ‘ output’ equations u = h*(x*, u*, e, ė,…) and x equals; h* * (x*, e, ė…) is studied. Instead of an extension of the linear matrix-oriented singular system theory, the non-linear system inversion ideas are found to be easily applicable, to preserve much of the original system structure, and to give insight into the possibly distributional behaviour of and the possible incompatibilities in the system.