LPV and LTV Models

R2026b

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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Model Objects

`lpvss`	Linear parameter-varying state-space model (Since R2023a)
`ltvss`	Linear time-varying state-space model (Since R2023a)
`getTestValue`	Access test values for validating data function (Since R2023a)
`setTestValue`	Modify test values for validating data function (Since R2023a)
`findop`	Compute operating condition from specifications (Since R2023b)
`fixInput`	Fix value of some inputs and delete them (Since R2024a)

Sampling and Interpolation

`psample`	Sample linear parameter-varying or time-varying dynamics (Since R2024a)
`ssInterpolant`	Build gridded LTV or LPV model from state-space data (Since R2023a)

Time Response Simulation

`step`	Step response of dynamic system
`impulse`	Impulse response plot of dynamic system; impulse response data
`lsim`	Compute time response simulation data of dynamic system to arbitrary inputs
`initial`	System response to initial states of state-space model
`RespConfig`	(Not recommended) Options for step or impulse responses (Since R2023a)

Model Interconnection

`feedback`	Feedback connection of multiple models
`connect`	Block diagram interconnections of dynamic systems
`series`	Series connection of two models
`parallel`	Parallel connection of two models
`lft`	Generalized feedback interconnection of two models (Redheffer star product)

Model Transformation

`c2d`	Convert model from continuous to discrete time
`d2c`	Convert model from discrete to continuous time
`d2d`	Resample discrete-time model
`xperm`	Reorder states in state-space models
`sminreal`	Eliminates structurally disconnected states, delays, and blocks

Blocks

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LPV Simulation

	LPV System	Simulate linear parameter-varying (LPV) systems
	LTV System	Simulate linear time-varying (LTV) systems (Since R2024a)

Continuous-Time Varying Systems

	Varying Delay	Varying delay with support for fixed delay and zero delay (direct feedthrough) (Since R2024a)
	Varying Lowpass Filter	Butterworth filter with varying coefficients
	Varying Notch Filter	Notch filter with varying coefficients
	PID Controller	Continuous-time or discrete-time PID controller
	PID Controller (2DOF)	Continuous-time or discrete-time two-degree-of-freedom PID controller
	Varying Transfer Function	Transfer function with varying coefficients
	Varying State Space	State-space model with varying matrix values
	Varying Observer Form	Observer-form state-space model with varying matrix values

Discrete-Time Varying Systems

	Discrete Varying Delay	Discrete varying delay with support for fixed delay and zero delay (direct feedthrough) (Since R2024a)
	Discrete Varying Lowpass	Discrete Butterworth filter with varying coefficients
	Discrete Varying Notch	Discrete-time notch filter with varying coefficients
	Discrete PID Controller (2DOF)	Discrete-time or continuous-time two-degree-of-freedom PID controller
	Discrete PID Controller	Discrete-time or continuous-time PID controller
	Discrete Varying Transfer Function	Discrete-time transfer function with varying coefficients
	Discrete Varying State Space	Discrete-time state-space model with varying matrix values
	Discrete Varying Observer Form	Discrete-time observer-form state-space model with varying matrix values

Topics

LTV and LPV Model Basics

LTV and LPV Modeling
Fundamentals of linear time-varying and parameter-varying models.
Using LTV and LPV Models in MATLAB and Simulink
Create, analyze, and simulate linear parameter-varying and linear time-varying state-space models.

Using Analytic LTV and LPV Models

LPV Model of Bouncing Ball
Construct an LPV representation of a system that exhibits multi-mode dynamics.
LPV Model of Engine Throttle
Model engine throttle behavior as a linear parameter-varying system.
Analysis of Gain-Scheduled PI Controller
Analyze gain-scheduled PI control of an LPV system.
LPV Model of Magnetic Levitation System
Create analytic LPV model from linearized equations of magnetic levitation system.
Gain-Scheduled LQG Controller
Demonstrate instability in gain-scheduled control when parameters vary too quickly.

Using Gridded LTV and LPV Models

LPV Approximation of Boost Converter Model
Obtain linear parameter-varying approximation of a nonlinear Simscape™ Electrical™ model.
Design and Validate Gain-Scheduled Controller for Nonlinear Aircraft Pitch Dynamics
Approximate nonlinear behavior of airframe pitch axis dynamics using linear parameter-varying model.
LPV Model of Magnetic Levitation Model from Batch Linearization Results
Create a gridded LPV model from batch linearization results of a magnetic levitation model.
Reduced Order Modeling of a Nonlinear Dynamical System as an Identified Linear Parameter Varying Model (System Identification Toolbox)
Identify a linear parameter varying reduced order model of a cascade of nonlinear mass-spring-damper systems.