Is there any in-built function/ method to customize state-space model in MATLAB

If the state space model is of the form:

dx/dt = Ax + Bu

y = Cx + Du

we can easily assign the values of A, B, C, D in matlab and get a transfer function using the ss and tf commands.

However if the state space model is of the form say:

dx/dt = Ax + Bu*e^t

y = Cx + Du*e^t

y(t) = 0 for all t>=0

and Cx + Du*e^t = 0 for all t>=0

Do we have any in-built function in MATLAB through we can customize our state-space model and the provide the values of A, B, C, D to get our transfer function G?

[Paul]

What do you mean by

u*e^t

Is that convolution or multiplication?

Also, the constraint y(t) = 0 is confusing. I mean, if y(t) = 0, then the transfer function is zero (assuming an LTI system).

[Siddhanth Sunil Shah]

u*e^t is actually a multiplication. Its Bue^t.

Yes that is what I thought too that the transfer function should be zero but apparently it should'nt be and should be possible using the eigen value formulation of the state space representation.

Answer 1

[Kartik Saxena]

Hi,

In MATLAB, the standard state-space to transfer function conversion using `ss` and `tf` commands assumes a linear time-invariant (LTI) system. The system you've described includes a time-varying element `e^t` in the input matrix and direct transmission matrix, which makes it a time-varying system. MATLAB's Control System Toolbox does not directly support conversion of time-varying state-space models to transfer functions using built-in commands.

However, you can represent time-varying systems using functions or handle classes to create custom behavior. Here's a general approach to simulate such systems:

1. Define the System Matrices as Functions: You can define `A`, `B`, `C`, and `D` as functions of time if they vary with time. In your case, `B(t) = B*e^t` and `D(t) = D*e^t`.

2. Simulate the System: Use MATLAB's numerical solvers (like `ode45`) to simulate the system's response to an input. You'll need to define the differential equations in a function that the solver can use.

I hope this resolves your issue.