Control System Toolbox

Chapter 1
Reference

This chapter contains detailed descriptions of all Control System Toolbox functions. It begins with a list of functions grouped by subject area and continues with the reference entries in alphabetical order. Information is also available through the online Help facility.

Category Tables

**Table 1-1: LTI Models**
Function Name	Description
`drss`	Generate random discrete state-space model.
`dss`	Create descriptor state-space model.
`filt`	Create discrete filter with DSP convention.
`frd`	Create a frequency response data (FRD) model.
`frdata`	Retrieve data from an FRD model.
`get`	Query LTI model properties.
`ltimodels`	Information on LTI models
`ltiprops`	Information on all LTI properties.
`set`	Set LTI model properties.
`rss`	Generate random continuous state-space model.
`ss`	Create state-space model.
`ssdata, dssdata`	Retrieve state-space data.
`tf`	Create transfer function.
`tfdata`	Retrieve transfer function data.
`totaldelay`	Provide the aggregate delay for an LTI model.
`zpk`	Create zero-pole-gain model.
`zpkdata`	Retrieve zero-pole-gain data.

**Table 1-2: Model Characteristics**
Function Name	Description
`class`	Display model type (`'tf'`, `'zpk'`, `'ss',` or `'frd'`).
`hasdelay`	Test true if LTI model has any type of delay.
`isa`	Test true if LTI model is of specified type.
`isct`	Test true for continuous-time models.
`isdt`	Test true for discrete-time models.
`isempty`	Test true for empty LTI models.
`isproper`	Test true for proper LTI models.
`issiso`	Test true for SISO models.
`ndims`	Display the number of model/array dimensions.
`size`	Display output/input/array dimensions.

**Table 1-3: Model Conversion**
Function Name	Description
`c2d`	Convert from continuous- to discrete-time models.
`chgunits`	Convert the `units` property for FRD models.
`d2c`	Convert from discrete- to continuous-time models.
`d2d`	Resample discrete-time models.
`delay2z`	Convert delays in discrete-time models or FRD models.
`frd`	Convert to a frequency response data model.
`pade`	Compute the Padé approximation of delays.
`reshape`	Change the shape of an LTI array
`residue`	Provide partial fraction expansion (see Using MATLAB).
`ss`	Convert to a state space model.
`tf`	Convert to a transfer function model.
`zpk`	Convert to a zero-pole-gain model.

**Table 1-4: Model Order Reduction**
Function Name	Description
`balreal`	Calculate an I/O balanced realization.
`minreal`	Calculate minimal realization or pole/zero cancellation.
`modred`	Delete states in I/O balanced realization.
`sminreal`	Calculate structured model reduction.

**Table 1-5: State-Space Realizations**
Function Name	Description
`canon`	Canonical state-space realizations.
`ctrb`	Controllability matrix.
`ctrbf`	Controllability staircase form.
`gram`	Controllability and observability gramians.
`obsv`	Observability matrix.
`obsvf`	Observability staircase form.
`ss2ss`	State coordinate transformation.
`ssbal`	Diagonal balancing of state-space realizations.

**Table 1-6: Model Dynamics**
Function Name	Description
`damp`	Calculate natural frequency and damping.
`dcgain`	Calculate low-frequency (DC) gain.
`covar`	Calculate covariance of response to white noise.
`dsort`	Sort discrete-time poles by magnitude.
`esort`	Sort continuous-time poles by real part.
`norm`	Calculate norms of LTI models ( and ).
`pole, eig`	Calculate the poles of an LTI model.
`pzmap`	Plot the pole/zero map of an LTI model.
`roots`	Calculate roots of polynomial (see Using MATLAB).
`zero`	Calculate zeros of an LTI model.

Table 1-7: **Model Building**
Function Name	Description
`append`	Append models in a block diagonal configuration.
`augstate`	Augment output by appending states.
`connect`	Connect the subsystems of a block-diagonal model according to an interconnection scheme of your choice.
`conv`	Convolve two polynomials (see Using MATLAB).
`drmodel, drss`	Generate random discrete-time model.
`feedback`	Calculate the feedback connection of models.
`lft`	Calculate the star product (LFT interconnection).
`ord2`	Generate second-order model.
`pade`	Compute the Padé approximation of time delays.
`parallel`	Create a generalized parallel connection.
`rmodel, rss`	Generate random continuous model.
`series`	Create a generalized series connection.
`stack`	Concatenate LTI models along array dimensions.

**Table 1-8: Time Response**
Function Name	Description
`filter`	Simulate discrete SISO filter (see Using MATLAB).
`gensig`	Generate an input signal.
`impulse`	Calculate impulse response.
`initial`	Calculate initial condition response.
`lsim`	Simulate response of LTI model to arbitrary inputs.
`ltiview`	Open the LTI Viewer for linear response analysis.
`step`	Calculate step response.

**Table 1-9: Frequency Response**
Function Name	Description
`bode`	Calculate bode plot.
`evalfr`	Evaluate response at single complex frequency.
`freqresp`	Evaluate frequency response for selected frequencies.
`linspace`	Create a vector of evenly spaced frequencies.
`logspace`	Create a vector of logarithmically spaced frequencies.
`ltiview`	Open the LTI Viewer for linear response analysis.
`margin`	Calculate gain and phase margins.
`ngrid`	Superimpose grid lines on a Nichols plot.
`nichols`	Calculate Nichols plot.
`nyquist`	Calculate Nyquist plot.
`pzmap`	Calculate pole/zero map.
`rlocus`	Calculate root locus.
`rlocfind`	Find gain/pole on root locus.
`rltool`	Open Root Locus Design GUI.
`sgrid`	Superimpose s-plane grid on root locus or pole/zero map.
`sigma`	Calculate singular value plot.
`zgrid`	Superimpose z-plane grid on root locus or pole/zero map.

**Table 1-10: Pole Placement**
Function Name	Description
`acker`	Calculate SISO pole placement design.
`place`	Calculate MIMO pole placement design.
`estim`	Form state estimator given estimator gain.
`reg`	Form output-feedback compensator given state-feedback and estimator gains.
`rltool`	Open Root Locus Design GUI

**Table 1-11: LQG Design**
Function Name	Description
`lqr`	Calculate the LQ-optimal gain for continuous models.
`dlqr`	Calculate the LQ-optimal gain for discrete models.
`lqry`	Calculate the LQ-optimal gain with output weighting.
`lqrd`	Calculate the discrete LQ gain for continuous models.
`kalman`	Calculate the Kalman estimator.
`kalmd`	Calculate the discrete Kalman estimator for continuous models.
`lqgreg`	Form LQG regulator given LQ gain and Kalman filter.

**Table 1-12: Equation Solvers**
Function Name	Description
`care`	Solve continuous-time algebraic Riccati equations.
`dare`	Solve discrete-time algebraic Riccati equations.
`lyap`	Solve continuous-time Lyapunov equations.
`dlyap`	Solve discrete-time Lyapunov equations.

**Table 1-13: Graphical User Interfaces for Model Analysis and Design**
Function Name	Description
`ltiview`	Open the LTI Viewer for linear response analysis.
`rltool`	Open the Root Locus Design GUI.

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Chapter 1Reference

Chapter 1
Reference