Deterministic identification of lossless and dissipative systems

We illustrate procedures to identify a state-space representation of a passive or bounded-real system from noisefree measurements. The basic idea underlying our algorithms is to obtain a state sequence from a rank-revealing factorization of a Gramian-like matrix constructed from the data. The computation of state-space equations is then performed solving a system of linear equations, similarly to what happens in classical deterministic subspace identification methods. I. PROBLEM STATEMENT We consider the following problem. We are given a discrete-time w-dimensional trajectory w consisting of inputs u and outputs y, which we know is produced by a linear finite-dimensional time-invariant system which is passiveor bounded-real. Moreover, we assume that certain identifiability conditions (described further in the paper) are satisfied. The problem is to find a state-space description of the system. In order to solve this problem, we could use subspace identification methods (see [7]) to compute a state-space sequence x from the data w, and then proceed to solve for (A,B,C,D) in the equations [ σx