Nonfragile H_∞ control for periodic stochastic systems with probabilistic measurement

Area of Science:

• Control Theory
• Stochastic Systems
• System Stability

Background:

• Periodic stochastic systems are susceptible to performance degradation due to time delays and probabilistic measurements.
• Ensuring robust control under these conditions is crucial for reliable system operation.

Purpose of the Study:

• To develop a nonfragile H_∞ control strategy for periodic stochastic systems with probabilistic measurement uncertainty.
• To enhance system stability and performance by addressing time delays and their rates of change.

Main Methods:

• Formulation of a novel Lyapunov-Krasovskii functional that incorporates time delay and its rate.
• Employment of mode-dependent stochastic variables to account for probabilistic measurement characteristics.
• Derivation of new sufficient conditions for guaranteed stability and performance.

Main Results:

• The proposed Lyapunov-Krasovskii functional effectively utilizes delay information.
• The use of mode-dependent stochastic variables leads to improved control design.
• New sufficient conditions for nonfragile H_∞ control were successfully derived.

Conclusions:

• The developed control design is effective for periodic stochastic systems with probabilistic measurements.
• The novel approach provides a robust solution for managing system uncertainties and delays.
• Numerical examples validate the effectiveness of the proposed control strategy.