A Lyapunov–Krasovskii Functional Approach to Stability and Linear Feedback Synchronization Control for Nonlinear Multi-Agent Systems with Mixed Time Delays

Algorithm 1

Algorithm to design the linear feedback control.

	Algorithm
	Step 1. Initialize the system parameters and some positive constants , and
	Step 2. Select an appropriate matrix according to Assumption 1
	Step 3. Choose the control gain matrix
	Step 4. There exists positive scalars , symmetric matrices , any matrix , and LMI (52) hold
	If success, the procedure further moves to next step
	Otherwise, the procedure turns back to adjust the system parameters and control gain matrix in Step 1 and Step 3
	Step 5. Based on the proper control gain matrix, we design a linear feedback control