Normal Forms of Linear Time-Varying Systems With Applications to Output-Feedback Stabilization and Tracking
IEEE Transactions on Cybernetics
|April 28, 2025
Summary
This study introduces a normal form for multiple-input-multiple-output linear time-varying systems. This normal form aids in analyzing system dynamics and designing controllers for stabilization and tracking.
Area of Science:
- Control Theory
- System Dynamics
- Nonlinear Control
Background:
- Linear time-varying (LTV) systems are fundamental in control theory.
- Multiple-input-multiple-output (MIMO) systems present unique challenges due to interdependencies.
- Existing methods for normal forms may not apply to LTV MIMO systems with non-uniform relative degrees.
Purpose of the Study:
- To derive a normal form for MIMO LTV systems.
- To investigate the internal and external dynamics, and the inverse system.
- To parameterize zero dynamics and resolve stabilization and tracking problems.
Main Methods:
- Utilizing a linear time-varying (LTV) transformation.
- Developing a general relative degree concept for LTV MIMO systems.
- Applying the derived normal form for controller design.
Main Results:
- A novel normal form for MIMO LTV systems is presented.
- Internal/external dynamics, inverse system, and zero dynamics are characterized.
- Proportional-derivative (PD) output-feedback stabilization and tracking are achieved.
Conclusions:
- The proposed LTV normal form provides a systematic approach for analyzing and controlling complex MIMO LTV systems.
- The method effectively addresses stabilization and output tracking challenges.
- The illustrative example validates the practical applicability of the developed controllers.
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