balreal

Gramian-based balancing of state-space realizations.

📝 Syntax

• [sysb, g] = balreal(sys)

• [sysb, g, T, Ti] = balreal(sys)

📥 Input argument

• sys - LTI model.

📤 Output argument

• sysb - LTI model.

• g - Diagonal vector of the balanced Gramian matrix.

• T - State similarity transform matrix.

• Ti - State similarity transform inverse matrix.

📄 Description

balreal(sys) calculates a balanced realization, denoted as sysb, for the stable segment of the linear time-invariant (LTI) model sys.

This process is applicable to both continuous and discrete systems. If sys is not initially in state-space form, the function automatically converts it to state space using ss before proceeding with the balanced realization.

💡 Example

sys = ss([-1, 0; 0.1, -3], [1, 0]', [0, 1], 0);
[sysb, g, T, Ti] = balreal(sys)

🔗 See also

gram.

🕔 History

Version	📄 Description
1.0.0	initial version