Linear dynamical systems are a common way to (approximately) model the behavior of physical phenomena, via recurrence
Question:
Linear dynamical systems are a common way to (approximately) model the behavior of physical phenomena, via recurrence equations of the form2
where t is the (discrete) time, x(t) ∈ Rn describes the state of the system at time t, u(t) ∈ Rp is the input vector, and y(t) ∈ Rm is the output vector. Here, matrices A, B, C, are given.
1. Assuming that the system has initial condition x(0) = 0, express the output vector at time T as a linear function of u(0), . . . , u( T – 1); that is, determine a matrix H such that y(T) = HU(T), where contains all the inputs up to and including at time T – 1.
2. What is the interpretation of the range of H?
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Optimization Models
ISBN: 9781107050877
1st Edition
Authors: Giuseppe C. Calafiore, Laurent El Ghaoui
Question Posted: