On Singular Implicit Linear Dynamical Systems
Pierre Bernhard · SIAM Journal on Control and Optimization · 1982
We investigate properties of existence, unicity, representation, of the (causal) solutions of implicit linear systems (or “generalized systems”) when the underlying matrix pencil is singular. We relate the geometric and the algebraic approaches. The main conclusion is that if the underlying matrix pencil is “column singular” (i.e., has a nonempty set of column minimal indices) the causal solutions, when they exist, can exactly be represented as the output of a classical two-player dynamical system, where the second player accounts for the nonunicity. Properties of the equivalent system are related to those of the singular matrix pencils made with the given matrices.