New results on stability and H_∞ performance analysis for aperiodic sampled-data systems via augmented Lyapunov...

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Aperiodic sampled-data systems present challenges in stability and H∞ performance analysis.
• Lyapunov-Krasovskii theory and augmented Lyapunov functionals are standard approaches.
• Existing methods can be conservative, limiting their applicability.

Purpose of the Study:

• To develop a less conservative method for analyzing stability and H∞ performance.
• To improve the analysis of aperiodic sampled-data systems.
• To introduce an enhanced Lyapunov functional for more accurate system evaluation.

Main Methods:

• Utilizing an improved augmented Lyapunov functional.
• Incorporating the double-side looped-functional technique.
• Focusing on sampling-instant-dependent state variables for reduced conservatism.

Main Results:

• The proposed Lyapunov functional captures state variables more comprehensively.
• Sufficient cross-terms are generated, leading to reduced conservatism.
• The method provides less conservative results for stability and H∞ performance analysis.

Conclusions:

• The enhanced Lyapunov functional offers superior performance analysis for aperiodic systems.
• The proposed approach effectively reduces conservatism in stability analysis.
• Numerical examples confirm the superiority of the developed methods.