Digital control systems with random but bounded delays in the feedback loop can be modeled as finite-dimensional, discrete-time jump linear systems, with the transition jumps being modeled as finite-state Markov chains. This type of system can be called a “stochastic hybrid system”. Due to the structure of the augmented state-space model, control of such a system is an output feedback problem, even if a state feedback law is intended for the original system. We present a VK iteration algorithm to design switching and non-switching controllers for such systems. This algorithm uses an outer iteration loop to perturb the transition probability matrix. Inside this loop, one or more steps of V-K iteration is used to do controller synthesis, which requires the solution of two convex optimization problems constrained by LMI's.

}, author = {Lin Xiao and Arash Hassibi and Jonathan P. How}, booktitle = {Proceedings of the American Control Conference, 2000.}, month = {June}, pages = {2199-2204}, title = {Control with random communication delays via a discrete-time jump system approach}, url = {http://research.microsoft.com/apps/pubs/default.aspx?id=198378}, volume = {3}, year = {2000}, }