# Linear dynamical systems are a common way to (approximately) model the behavior of physical phenomena, via recurrence equations of the

## 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) ∈ Ris 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?

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Related Book For ## Optimization Models

ISBN: 9781107050877

1st Edition

Authors: Giuseppe C. Calafiore, Laurent El Ghaoui

Question Details
Chapter # 3
Section: EXERCISE
Problem: 4
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