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LPV and LTV Models

Linear parameter-varying and linear time-varying models

Create, manipulate, analyze, and simulate linear parameter-varying (LPV) and linear time-varying models (LTV). These models can approximate nonlinear systems and allow you to efficiently apply linear design techniques to nonlinear models.

With the available functionality, you can:

  • Create LPV or LTV models from mathematical expressions.

  • Create LPV or LTV models that interpolate linearization results over a grid of operating conditions.

  • Simulate time response.

  • Specify signal-based connections between varying models and with LTI models.

  • Sample dynamics over a grid of parameters to obtain local LTI approximations.

  • Discretize and resample LPV or LTV models.

Functions

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lpvssLinear parameter-varying state-space model (Since R2023a)
ltvssLinear time-varying state-space model (Since R2023a)
getTestValueAccess test values for validating data function (Since R2023a)
setTestValueModify test values for validating data function (Since R2023a)
findopCompute operating condition from specifications (Since R2023b)
fixInput Fix value of some inputs and delete them (Since R2024a)
psampleSample linear parameter-varying or time-varying dynamics (Since R2024a)
ssInterpolantBuild gridded LTV or LPV model from state-space data (Since R2023a)
stepStep response of dynamic system
impulseImpulse response plot of dynamic system; impulse response data
lsimPlot simulated time response of dynamic system to arbitrary inputs; simulated response data
initialSystem response to initial states of state-space model
RespConfigOptions for step or impulse responses (Since R2023a)
feedbackFeedback connection of multiple models
connectBlock diagram interconnections of dynamic systems
seriesSeries connection of two models
parallelParallel connection of two models
lftGeneralized feedback interconnection of two models (Redheffer star product)
c2dConvert model from continuous to discrete time
d2cConvert model from discrete to continuous time
d2dResample discrete-time model
xperm Reorder states in state-space models
sminrealEliminates structurally disconnected states, delays, and blocks

Blocks

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LPV SystemSimulate linear parameter-varying (LPV) systems
LTV SystemSimulate linear time-varying (LTV) systems (Since R2024a)
Varying DelayVarying delay with support for fixed delay and zero delay (direct feedthrough) (Since R2024a)
Varying Lowpass FilterButterworth filter with varying coefficients
Varying Notch FilterNotch filter with varying coefficients
PID ControllerContinuous-time or discrete-time PID controller
PID Controller (2DOF)Continuous-time or discrete-time two-degree-of-freedom PID controller
Varying Transfer FunctionTransfer function with varying coefficients
Varying State SpaceState-space model with varying matrix values
Varying Observer FormObserver-form state-space model with varying matrix values
Discrete Varying DelayDiscrete varying delay with support for fixed delay and zero delay (direct feedthrough) (Since R2024a)
Discrete Varying LowpassDiscrete Butterworth filter with varying coefficients
Discrete Varying NotchDiscrete-time notch filter with varying coefficients
Discrete PID Controller (2DOF)Discrete-time or continuous-time two-degree-of-freedom PID controller
Discrete PID ControllerDiscrete-time or continuous-time PID controller
Discrete Varying Transfer FunctionDiscrete-time transfer function with varying coefficients
Discrete Varying State SpaceDiscrete-time state-space model with varying matrix values
Discrete Varying Observer FormDiscrete-time observer-form state-space model with varying matrix values

Topics

LTV and LPV Model Basics

Using Analytic LTV and LPV Models

Using Gridded LTV and LPV Models