State-Space SISO Discrete Model

Overview

state_space_siso_discrete is FluxGraph's built-in structured-parameter model for discrete-time linear state-space systems:

1. x[k+1] = A_d x[k] + B_d u[k]
2. y[k] = C x[k] + D u[k]

This model is discrete by definition and does not use integration_method.

Parameters

Parameter	Type	Shape	Description
A_d	array	n x n	State transition matrix (square, finite values)
B_d	array	n	Input matrix/vector (finite values)
C	array	n	Output matrix/vector (finite values)
D	number	scalar	Direct feedthrough term (finite value)
x0	array	n	Initial state (finite values)
input_signal	string	-	Input signal path
output_signal	string	-	Output signal path

Validation is compile-time and path-specific:

1. A_d must be non-empty, rectangular, and square.
2. B_d, C, and x0 must match A_d dimension.
3. Ragged arrays and non-finite numbers are rejected.

Dimensional Policy

In strict dimensional mode:

1. input_signal and output_signal must have declared signal contracts.
2. The model does not impose a fixed unit symbol for those signals.

Current limitation:

1. Internal state-unit algebra is currently out of scope.
2. FluxGraph validates signal contracts at model boundaries, not matrix-level coefficient units.

Non-Goals

The following are intentionally out of scope for this model:

1. Continuous-time generic state-space (x_dot = A x + B u).
2. MIMO generalized matrices.
3. Structured command argument transport over runtime command APIs.

C++ Example

fluxgraph::ModelSpec model;
model.id = "ss";
model.type = "state_space_siso_discrete";
model.params["output_signal"] = std::string("ss.y");
model.params["input_signal"] = std::string("ss.u");
model.params["A_d"] = fluxgraph::ParamArray{
    fluxgraph::ParamArray{0.9, 0.1},
    fluxgraph::ParamArray{0.0, 0.95},
};
model.params["B_d"] = fluxgraph::ParamArray{0.1, 0.05};
model.params["C"] = fluxgraph::ParamArray{1.0, 0.0};
model.params["D"] = 0.0;
model.params["x0"] = fluxgraph::ParamArray{0.0, 0.0};

Runnable example:

1. examples/10_state_space_siso_discrete/

Loader-based examples:

1. examples/03_json_graph/state_space_siso_discrete.json
2. examples/04_yaml_graph/state_space_siso_discrete.yaml