Robust Static Output-Feedback Control for MJLS with Non-Homogeneous Markov Chains: A Comparative Study Considering a Wireless Sensor Network with Time-Varying PER

This paper deals with the problem of control through a semi-reliable communication channel, such as wireless sensor networks (WSN). Particularly, the case investigated is the one where the packet loss rate of the network is time-varying due to, for instance, variation in the distance between the nodes. Considering this practical motivation, the control system is modeled using a formulation based on discrete-time Markov jump linear systems (MJLS) with non-homogeneous Markov chains (time-varying transition probabilities). New control design conditions based on parameter-dependent linear matrix inequalities are proposed in order to solve this problem. The purpose is to demonstrate that this strategy is suitable to handle the networked control problem by comparing the temporal behavior of the closed-loop system with the Markovian controller and a standard proportional-integral-derivative (PID) controller. The case study presented in the paper considers the problem of the remote control of a Vertical Take-Off and Landing (VTOL) vehicle through a wireless communication channel. The network packet loss model employed in the case study is based on data collected on a wireless network workbench, which was previously developed and validated by the authors.

Robust H∞ Control of Markov Jump Linear Systems with Uncertain Switching Probabilities

В статье исследуется проблема робастного управления H∞ для систем с марковскими скачками и неопределенными матрицами интенсивностей перехода. Для рассматриваемой системы предлагается использовать робастный критерий качества управления H∞. На первом этапе проводится анализ характеристик робастного управления H∞ на основе сопряженных линейных матричных неравенств, далее решается задача выпуклой оптимизации с ограничениями, определенными в терминах разрешимости линейных матричных неравенств. На основе решения задачи оптимизации определено условие робастной стохастической устойчивости для систем с обратной связью, которое минимизирует уровень затухания возмущений. На основе рассматриваемого критерия спроектирован контроллер, который гарантирует робастное управление H∞ системой с обратной связью. Все условия выражаются в терминах линейных матричных неравенств, и, следовательно, они могут быть определены решателем линейных матричных неравенств. Представлен численный пример решения задачи, демонстрирующий эффективность предложенного метода робастного управления стохастической системы с марковскими скачкам.

Robust Stability of Time-Varying Markov Jump Linear Systems with Respect to a Class of Structured, Stochastic, Nonlinear Parametric Uncertainties

This note is devoted to a robust stability analysis, as well as to the problem of the robust stabilization of a class of continuous-time Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to effectively address the multi-perturbations case, we use scaling techniques. These techniques allow us to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov differential equations. A second characterization is given in terms of the existence of positive solutions of adequately defined parameterized backward Lyapunov differential inequalities. This second result is then exploited in order to solve a robust control synthesis problem.