Delay-Dependent Algebraic Riccati Equation to Stabilization of Networked Control Systems: Continuous-Time Case

Area of Science:

• Control Systems Engineering
• Systems Theory
• Networked Systems

Background:

• Networked control systems (NCS) often involve communication delays and signal attenuation.
• Previous studies frequently assumed ideal transmission with zero delay and infinite precision.
• Real-world NCS require addressing practical constraints like simultaneous delay and attenuation.

Purpose of the Study:

• To develop a delay-dependent algebraic Riccati equation (DARE) approach for mean-square stabilization of continuous-time NCS.
• To address the challenges of signal attenuation and transmission delay in control signal communication.
• To establish novel theoretical conditions and methods for analyzing NCS stability under these constraints.

Main Methods:

• Utilizing a delay-dependent algebraic Riccati equation (DARE) framework.
• Applying operator spectrum theory to analyze the stabilizing solutions of DAREs.
• Defining a delay-dependent Lyapunov operator for existence theorems.
• Deriving explicit maximal allowable delay bounds for scalar systems.

Main Results:

• A necessary and sufficient condition for mean-square stabilization is established, based on a unique positive definite solution to a DARE.
• The Lyapunov/spectrum stabilizing criterion is derived from this condition.
• An existence theorem for a unique stabilizing solution to a generalized DARE is proposed using a delay-dependent Lyapunov operator.
• The explicit maximal allowable delay bound for a scalar system is derived.

Conclusions:

• The proposed DARE approach provides a robust framework for analyzing and stabilizing NCS with communication constraints.
• The derived conditions and methods offer theoretical guarantees for system stability under delay and attenuation.
• The results are validated through illustrative examples, confirming the practical applicability of the theoretical findings.