Constrained hybrid control for parametric uncertainty systems via step-function method.

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Real-world signal transmission is prone to interruptions and errors, necessitating robust control system models.
• Existing control methods may not adequately address parametric uncertainty and impulsive control signals under saturation.

Purpose of the Study:

• To develop a novel class of parametric uncertainty hybrid control system models that realistically incorporate impulsive control signals and saturated inputs.
• To derive less conservative stability conditions compared to traditional Lyapunov methods.
• To design control gains and auxiliary control gains for practical implementation and to estimate attraction domains.

Main Methods:

• Utilized a step-function method for analysis.
• Employed an improved polytopic representation approach.
• Applied the Schur complement for deriving stability conditions.

Main Results:

• Established novel stability conditions for the proposed hybrid control system models.
• Developed a systematic approach for designing control and auxiliary control gains.
• Demonstrated the applicability to fixed-time impulse problems, including systems with Zeno behavior.

Conclusions:

• The proposed methods provide less conservative stability criteria for uncertain hybrid control systems with impulsive and saturated signals.
• The developed control gain design facilitates practical stabilization of complex systems.
• Simulation results on uncertain neural network systems validate the effectiveness of the step-function-based stabilization methods.