# Direct Design of Controllers Using Complementary State and State-Derivative Feedback

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## Abstract

This paper is concerned with controllers design using complementary state and state-derivative feedback, as an extension of the work presented in Rossi et al. (in: Proceedings of XXI Congresso Brasileiro de Automática, Vitória, Brazil, pp 828–833, 2016). The novel approach is more general, in that it enables the direct design of an CSSDF controller, dispensing with the need for a preliminary state feedback design. For this purpose, a discrete-time design model is derived to describe the plant dynamics in terms of the state and state-derivative combinations available for feedback. The resulting model can be used with existing discrete-time state-space methods for the design of linear or nonlinear control laws. Simulation examples are presented to illustrate the proposed design method within a model predictive control formulation.

## Keywords

Complementary state and state-derivative feedback Direct design Discrete time Model predictive control## Notes

### Acknowledgements

The main theoretical results presented in this paper were developed as part of the first author’s Ph.D. research (Rossi 2018), which was funded by CNPq under Doctoral Scholarship 140585/2014-1. The remaining authors acknowledge the support of FAPESP under Grant 2011/ 17610-0 and CNPq under Grants 303714/2014-0, 310798/2014-0, 301227/2017-9 (Research Fellowships).

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