Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

Filtering for discrete-time Markov jump systems with network transmitted mode

This paper is concerned with ℋ 2 and ℋ ∞ filter design for discrete-time Markov jump systems. The usual assumption of mode-dependent design, where the current Markov mode is available to the filter at every instant of time is substituted by the case where that availability is subject to another Markov chain. In other words, the mode is transmitted to the filter through a network with given transmission failure probabilities. The problem is solved by modeling a system with N modes as another with 2N modes and cluster availability. We also treat the case where the transition probabilities are not exactly known and demonstrate our conditions for calculating an ℋ ∞ norm bound are less conservative than the available results in the current literature. Numerical examples show the applicability of the proposed results. ©2010 IEEE.

Stochastic exponential stability of singular linear systems with Markov jump parameters

This paper deals with exponential stability of discrete-time singular systems with Markov jump parameters. We propose a set of coupled generalized Lyapunov equations (CGLE) that provides sufficient conditions to check this property for this class of systems. A method for solving the obtained CGLE is also presented, based on iterations of standard singular Lyapunov equations. We present also a numerical example to illustrate the effectiveness of the approach we are proposing.

Influence of a preventive training program on lower limb kinematics and vertical jump height of male volleyball athletes

Objective: To examine the influence of a preventative training program (PTP) on sagittal plane kinematics during different landing tasks and vertical jump height (VJH) in males. Design: Six weeks prospective exercise intervention. Participants: Fifteen male volleyball athletes (13 ± 0.7 years, 1.70 ± 0.12 m, 60 ± 12 kg). Interventions: PTP consisting of plyometric, balance and core stability exercises three times per week for six weeks. Bilateral vertical jumps with double leg (DL) and single leg (SL) landings were performed to measure the effects of training. Main outcome measurements: Kinematics of the knee and hip before and after training and VJH attained during both tasks after training. The hypothesis was that the PTP would produce improvements in VJH, but would not generate great changes in biomechanical behavior. Results: The only change identified for the SL was the longest duration of landing, which represents the time spent from initial ground contact to maximum knee flexion, after training, while increased angular displacement of the knee was observed during DL. The training did not significantly alter the VJH in either the SL (difference: 2.7 cm) or the DL conditions (difference: 3.5 cm). Conclusions: Despite the PTP's effectiveness in inducing some changes in kinematics, the changes were specific for each task, which highlights the importance of the specificity and individuality in selecting prevention injury exercises. Despite the absence of significant increases in the VJH, the absolute differences after training showed increases corroborating with the findings of statistically powerful studies that compared the results with control groups. The results suggest that short-term PTPs in low risk young male volleyball athletes may enhance performance and induce changes in some kinematic parameters. © 2012 Elsevier Ltd.