# 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 form^{2}

^{}

where t is the (discrete) time, x(t) ∈ R^{n} describes the state of the system at time t, u(t) ∈ R^{p }is the input vector, and y(t) ∈ R^{m}^{ }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

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