ϵ-Controllability/ϵ-Observability of linear switched sampled-data systems with the non-equidistant time schedule

Area of Science:

• Control Theory
• Systems Engineering
• Applied Mathematics

Background:

• Linear switched sampled-data systems present challenges in controllability and observability due to non-equidistant sampling.
• Existing methods often require a high number of sampling instances, limiting practical application.

Purpose of the Study:

• To develop novel concepts for analyzing controllability and observability in linear switched sampled-data systems.
• To introduce epsilon-controllability and epsilon-observability for systems with non-equidistant sampling schedules.
• To enable control and observation of systems with initial times outside the epsilon neighborhood of switching instants.

Main Methods:

• Introduction of two new notions: epsilon-controllability and epsilon-observability.
• Development of a theoretical framework for analyzing these properties under non-equidistant sampling.
• Numerical experiments on continuous-time switched linear systems to validate the concepts.

Main Results:

• Demonstrated that epsilon-controllability and epsilon-observability require fewer sampling times compared to traditional methods.
• Showcased the finite nature of sampling candidates for these properties as epsilon approaches zero.
• Validated the derived properties for various epsilon values using constructed non-equidistant sampling patterns.

Conclusions:

• The proposed epsilon-controllability and epsilon-observability offer a more feasible approach to analyzing linear switched sampled-data systems.
• These novel concepts provide a robust framework for controlling and observing such systems under complex sampling conditions.
• The findings have implications for the design and analysis of advanced control systems in various engineering domains.