PWA SYSTEM

Piecewise affine discrete-time dynamical system object.

Description
Syntax
Properties
Methods
See also
Acknowledgements

Description

The pwaSystem object describes a piecewise affine discrete-time dynamical system in the form: $x_{k+1} = A_i x_k + B_i u_k + f_i$ , being $x_k$ the state variable at time instant $k$ and $u_k$ the input variable of the system at the same time instant. The sampling time $T_s$ of the system can also be specified. The dynamics of the system are described by the matrices $A_i$ , $B_i$ and $f_i$ . The state and input variables 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

pwaSys = pwaSystem()

Builds an empty pwaSystem object.

pwaSys = pwaSystem(nx,nu,ndyn)

Builds a discrete-time piecewise affine system by specifying the number of states (nx) and inputs (nu). The matrices Ai, Bi and fi are filled with zeros.

Properties

nx - number of state variables.
nu - number of input variables.
nd - number of system dynamics.
Ts - sampling time.
A, B, f - cells containing matrices defining the discrete time PWA system $x_{k+1} = A_i x_k + B_i u_k + f_i$ , when $H_{i} \left[\begin{array}{c} x_{k}\\u_{k} \end{array} \right]\leq K_{i}$ .
H, K - cells containing matrices defining the regions
xnames - cell array of strings containing the names of the states.
unames - cell array of strings containing the names of the inputs.

Methods

disp - displays some information about the pwaSystem object.
getMatrices - gets the Ai, Bi and f_ matrices defining the PWA system.
getNumberOfInputs - gets the number of input variables.
getNumberOfStates - gets the number of state variables.
getSamplingTime - gets the sampling time of the system.
setInputNames - allows to give a mnemonical name to the input variables.
setMatrices - sets the Ai, Bi and fi matrices defining the linear system.
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:

Bart Genuit (b.a.g.genuit@tue.nl)
Alberto Oliveri (alberto.oliveri@unige.it)