Linear Time Invariant Models

Model Data Access

Model Conversions

Model Interconnections

Model Characteristics

Model Simplification

Time Domain Analysis

Frequency Domain Analysis

PID Control

Pole Placement

Optimal Control

Robust Control

Matrix Equation Solvers

Model Reduction

Controller Reduction

Experimental Data Handling

System Identification

Overloaded LTI Operators

Overloaded IDDATA Operators

Examples

Miscellaneous

Function Reference: gram

Function File: W = gram (sys, mode)

Function File: Wc = gram (a, b)

gram (sys, "c") returns the controllability gramian of the (continuous- or discrete-time) system sys. gram (sys, "o") returns the observability gramian of the (continuous- or discrete-time) system sys. gram (a, b) returns the controllability gramian Wc of the continuous-time system \(\dot{x} = A x + B u\) i.e., Wc satisfies \(A\, Wc + m Wc^T + B\,B^T = 0\)

Source Code: gram