# Control of bilinear systems using gain-scheduling: Stability and performance guarantees

arXiv: https://arxiv.org/abs/2304.04486 · HTML: https://mlsanity.com/paper/2304.04486/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2023.

## Built on by (most cited first, 2 of 2)

- [SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems](https://mlsanity.com/paper/2402.03145/) (2024)
- [End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data](https://mlsanity.com/paper/2409.18010/) (2024)

## Abstract (arXiv)

In this paper, we present a state-feedback controller design method for bilinear systems. To this end, we write the bilinear system as a linear fractional representation by interpreting the state in the bilinearity as a structured uncertainty. Based on that, we derive convex conditions in terms of linear matrix inequalities for the controller design, which are efficiently solvable by semidefinite programming. Further, we prove asymptotic stability and quadratic performance of the resulting closed-loop system locally in a predefined region. The proposed design uses gain-scheduling techniques and results in a state feedback with rational dependence on the state, which can substantially reduce conservatism and improve performance in comparison to a simpler, linear state feedback. Moreover, the design method is easily adaptable to various scenarios due to its modular formulation in the robust control framework. Finally, we apply the developed approaches to numerical examples and illustrate the benefits of the approach.