Overview

Given a linear model postulate of the form

we would like to investigate, in general, the identifiability of the parameters appearing in matrices A, B, C, and D, the initial conditions x ₀, and the zero shifts ? u and ? z. However, as discussed in Chapter 3, Sec. V.A, proper flight maneuvers ensure identifiability of aerodynamic derivatives, that is, of A, B, C, and D. Hence, we consider here the issue related to other constant terms x ₀, ? u and ? z only. They are in total ( n _x + n _u + n _y) in number, where n _x is the number of states, n _u the number of control inputs, and n _y the number of outputs. The state, control, and output variables are functions of time; however, we drop the time dependence, ( t), in the notation throughout this section.

Identifiability of any parameter in general is determined by the observability of the system. A system is said to be observable if the initial state x ₀ can be determined uniquely by examining the system output y( t) for t > t ₀ in a finite interval over some period of time 0 ? T. If the initial conditions are determined, the system behavior at any time t in the future is uniquely determined. To...