Equivalent transformation and weighted $H_\infty$-optimization of linear descriptor systems

TL;DR

This paper develops a method for transforming and optimizing linear descriptor systems using weighted $H__$-control, enabling application of standard techniques to complex systems with initial conditions.

Contribution

It introduces a non-degenerate transformation approach for descriptor systems, facilitating $H__$-optimization with a generalized performance measure.

Findings

Transformation simplifies the control design process.

The method effectively handles systems with non-zero initial vectors.

Numerical example demonstrates practical applicability.

Abstract

The problem of a generalized type of $H_\infty$-control is investigated for a class of admissible descriptor systems with a non-zero initial vector. A generalized performance measure is used, which characterizes the weighted damping level of external and initial disturbances. A non-degenerate transformation of the system is proposed, which allows to apply known methods for evaluation and the achievement of desired performance measures for conventional lower-order systems. A numerical example of a controlled hydraulic system with three tanks is given.