Performance analysis and controller improvement for linear systems with (m,k)-firm data losses

This paper describes methods for the analysis and design of control applications with real-time constraints, which allow data losses in the sensing-to-actuation path governed by the property of (m, k)-firmness. An automaton consisting of open- and closed-loop dynamics and a graph representing (m, k)-firmness defines the overall system behavior as a constrained switched linear system. The worst-case quadratic cost is analyzed for a given optimal linear quadratic regulator design. A simple analytic upper bounding method is compared to a method based on solving a (computationally more complex) semidefinite program. Furthermore, control design methods for performance improvement for the worst case are presented. A known LMI-based method is compared to an iterative controller improvement scheme inspired by ideas from dynamic programming. Conservatism and computational effort of the methods are discussed. A numerical example is used for illustration