A new look at the robust control of discrete-time Markov jump linear systems

* A preliminary version of this paper appeared in the Proceedings of the 52nd IEEE Conference on Decision and Control, 2013.

ABSTRACT

In this paper, we make a foray in the role played by a set of four operators on the study of robust H₂ and mixed H₂/H_∞ control problems for discrete-time Markov jump linear systems. These operators appear in the study of mean square stability for this class of systems. By means of new linear matrix inequality (LMI) characterisations of controllers, which include slack variables that, to some extent, separate the robustness and performance objectives, we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of H₂ performance. Since each operator provides a different degree of conservatism, the results are unified in the form of an iterative LMI technique for designing robust H₂ controllers, whose convergence is attained in a finite number of steps. The method yields a new way of computing mixed H₂/H_∞ controllers, whose conservatism decreases with iteration. Two numerical examples illustrate the applicability of the proposed results for the control of a small unmanned aerial vehicle, and for an underactuated robotic arm.

Keywords:

• Stochastic jump processes
• H₂/H_∞ control
• robustness
• unmanned aerial vehicles
• robotics

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. As indicated in the numerical examples of Section 5, there are situations in which this additional conservatism is negligible.

Additional information

Funding

This work was partially supported by the Brazilian national research council – CNPq [grant number 302501/2010-0], [grant number 458456/2014-4].