This brief presents a control strategy for Markov jump linear systems (MJLS) with no access to the Markov state (or mode). The controller is assumed to be in the linear state-feedback format and the aim of the control problem is to design a static mode-independent gain that minimizes a bound to the corresponding H ₂ -cost. This approach has a practical appeal since it is often difficult to measure or to estimate the actual operating mode. The result of the proposed method is compared with that of a previous design, and its usefulness is illustrated by an application that considers the velocity control of a DC motor device subject to abrupt failures that is modeled as an MJLS.

The note presents an algorithm for the average cost control problem of continuous-time Markov jump linear systems. The controller assumes a linear state-feedback form and the corresponding control gain does not depend on the Markov chain. In this scenario, the control problem is that of minimizing the long-run average cost. As an attempt to solve the problem, we derive a global convergent algorithm that generates a gain satisfying necessary optimality conditions. Our algorithm has practical implications, as illustrated by the experiments that were carried out to control an electronic dc-dc buck converter. The buck converter supplied a load that suffered abrupt changes driven by a homogeneous Markov chain. Besides, the source of the buck converter also suffered abrupt Markov-driven changes. The experimental results support the usefulness of our algorithm.

The stability and the problem of ℋ₂ guaranteed cost computation for discrete-time Markov jump linear systems (MJLS) are investigated, assuming that the transition probability matrix is not precisely known. It is generally difficult to estimate the exact transition matrix of the underlying Markov chain and the setting has a special interest for applications of MJLS. The exact matrix is assumed to belong to a polytopic domain made up by known probability matrices, and a sequence of linear matrix inequalities (LMIs) is proposed to verify the stability and to solve the ℋ₂ guaranteed cost with increasing precision. These LMI problems are connected to homogeneous polynomially parameter-dependent Lyapunov matrix of increasing degree g. The mean square stability (MSS) can be established by the method since the conditions that are sufficient, eventually turns out to also be necessary, provided that the degree g is large enough. The ℋ₂ guaranteed cost under MSS is also studied here, and an extension to cope with the problem of control design is also introduced. These conditions are only sufficient, but as the degree g increases, the conservativeness of the ℋ₂ guaranteed costs is reduced. Both mode-dependent and mode-independent control laws are addressed, and numerical examples illustrate the results.

This paper shows the construction of a low-cost, open-source mechanical ventilator. The motivation for constructing this kind of ventilator comes from the worldwide shortage of mechanical ventilators for treating COVID-19 patients—the COVID-19 pandemic has been striking hard in some regions, especially the deprived ones. Constructing a low-cost, open-source mechanical ventilator aims to mitigate the effects of this shortage on those regions. The equipment documented here employs commercial spare parts only. This paper also shows a numerical method for monitoring the patients’ pulmonary condition. The method considers pressure measurements from the inspiratory limb and alerts clinicians in real-time whether the patient is under a healthy or unhealthy situation. Experiments carried out in the laboratory that had emulated healthy and unhealthy patients illustrate the potential benefits of the derived mechanical ventilator.