# LINEAR SYSTEM

Linear discrete-time dynamical system object

## Contents

Class of MOBY-DIC TOOLBOX.

## Description

The linearSystem object describes a linear discrete-time dynamical system in the form: , being the state variable at time instant k, the input variable of the system at the same time instant and p an array of parameters. The sampling time of the system can also be specified. The dynamics of the system are described by the matrices A, B and f. The state and input variables as well as the parameters can be given mnemonic names for a easier comprehension of their meaning. A PWA function (one of the objects available in the toolbox) can be passed as input variable and then the circuit can be simulated and time evolutions of the variables can be plotted.

## Syntax

**linSys = linearSystem()**

Builds an empty linearSystem object.

**linSys = linearSystem(nx,nu,np)**

Builds a discrete-time linear system by specifying the number of states (nx), inputs (nu) and parameters (np). The matrices A, B, W and f have 0 values.

## Properties

- nx - number of state variables.
- nu - number of input variables.
- np - number of parameters.
- Ts - sampling time.
- A, B, W, f - matrices defining the discrete time linear system .
- xnames - cell array of strings containing the names of the states.
- unames - cell array of strings containing the names of the inputs.
- pnames - cell array of strings containing the names of the parameters.

## Methods

- disp - displays some information about the linearSystem object.
- getMatrices - gets the A, B and f matrices defining the linear system.
- getNumberOfInputs - gets the number of input variables.
- getNumberOfStates - gets the number of state variables.
- getNumberOfParameters - gets the number of parameters.
- getSamplingTime - gets the sampling time of the system.
- setInputNames - allows to give a mnemonical name to the input variables.
- setMatrices - sets the A, B and f matrices defining the linear system.
- setParameterNames - allows to give a mnemonical name to the parameters.
- setSamplingTime - sets the sampling time of the system.
- setStateNames - allows to give a mnemonical name to the state variables.
- sim - simulates the dynamical system.
- simplot - simulates the dynamical system and plots time evolution of states and inputs.

## Acknowledgements

Contributors:

- Alberto Oliveri (alberto.oliveri@unige.it)

Copyright is with:

- Copyright (C) 2011 University of Genoa, Italy.