State space systems

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Elec 302: state space systems overview

0.1 "the mars global surveyor"

1 Matrix inversion

2 Controllability

3 The concept of state

4 Controllability and observability grammians

5 Observability

6 Diagonalizability

7 Laplace example

8 Linear systems with constant coefficients

8.1 Analyzing linear constant coefficient systems

8.2 Non-zero initial conditions

9 Dynamical systems

10 Cayley-hamilton theorem

11 Eigenvalue decomposition

11.1 Multiplicity

11.2 Helpful facts

11.4 Symmetric matrices

12 Generating sets and bases

13 Matrix exponential

13.1 Definition

13.2 General method

13.3 Properties of the matrix exponential

14 Laplace properties and transforms

14.1 Laplace properties

14.2 Unilateral laplace transforms

15 Laplace domain solutions to state and output equations

16 Time domain state and output equations

17 Matrix inversion

18 Matrix representation of systems

18.1 State equations

18.2 Output equations

18.3 Compact system notation

19 Defining the state for an n-th order differential equation

20 Partial fraction expansion

20.1 Heaviside "cover-up" method

20.2 No repeated roots

20.3 Repeated roots

20.4 Finding partial fractions in matlab

21 Linear time invariant systems

21.1 Introduction

21.2 Linear time invariant systems

21.3 Linear systems

21.4 Time invariant systems

21.5 Linear time invariant systems

21.6 Lti systems in series

21.7 Lti systems in parallel

21.8 Linear time invariant demonstration

21.9 Lti systems summary

22 I/o and i/s/o relationships in time and frequency

22.1 I/o and i/s/o representation of siso linear systems

22.2 Definition of state from i/o description

22.3 Various responses

Source: OpenStax, State space systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10143/1.3

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