Basis transform in switched linear system state-space models from input-output data

This paper tackles the basis selection issue in the context of state-space hybrid system identification from input-output data. It is often the case that an identification scheme responsible for state-space switched linear system (SLS) estimation from input-output data operates on local levels. Such individually identified local estimates reside in distinct state bases, which call for the need to perform some basis correction mechanism that facilitates their coherent patching for the ultimate goal of performing output predictions for predefined input test signals. We derive necessary and sufficient conditions on the submodel set, the switching sequence, and the dwell times that guarantee the presented approach's success. Such conditions turn out to be relatively mild, which contributes to the application potential of the devised algorithm. We also provide a linkage between this work and the existing literature by providing several insightful remarks that highlight the discussed method's favorability. We supplement the theoretical findings by an elaborative numerical simulation that puts our methodology into action

Realization of multi-input/multi-output switched linear systems from Markov parameters

This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically equivalent to the true SLS is derived from the Markov parameters assuming that the submodels have a common MacMillan degree and a mild condition on their dwell times holds. In the second stage, zero sets of LTV Hankel matrices where the realized system has a linear time-invariant (LTI) pulse response matching that of the original SLS are exploited to extract the submodels, up to arbitrary similarity transformations, by a clustering algorithm using a statistics that is invariant to similarity transformations. Recovery is shown to be complete if the dwell times are sufficiently long and some mild identifiability conditions are met. In the third stage, the switching sequence is estimated by three schemes. The first scheme is based on forward/backward corrections and works on the short segments. The second scheme matches Markov parameter estimates to the true parameters for LTV systems and works on the medium-to-long segments. The third scheme also matches Markov parameters, but for LTI systems only and works on the very short segments. In the fourth stage, the submodels estimated in Stage~2 are brought to a common basis by applying a novel basis transformation method which is necessary before performing output predictions to given inputs. A numerical example illustrates the properties of the realization algorithm. A key role in this algorithm is played by time-dependent switching sequences that partition the state-space according to time, unlike many other works in the literature in which partitioning is state and/or input dependent

TÜRKIYE’DE YOĞUN BAKIM ÜNITELERINDE VENTILATÖR ILIŞKILI PNÖMONIYI ÖNLEMEK IÇIN ALINAN GÜNCEL ÖNLEMLER: TÜRK TORAKS DERNEĞI SOLUNUM YETMEZLIĞI VE YOĞUN BAKIM ÇALIŞMA GRUBU NOKTA PREVALANS ÇALIŞMASI

Objectives: The inadequate quality and nature of sleep is a commonly reported problem among hospitalized patients. The purpose of this study is to examine the effects of progressive muscle relaxation training program on sleep quality, sleep state, pain and life quality of patients who underwent pulmonary resection