Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters

Costa, Oswaldo Luiz do Valle; Fragoso, Marcelo D.

doi:10.1006/jmaa.1993.1341

Cited by 510 publications

(295 citation statements)

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“…The model proposed is inspired by piecewise deterministic jump systems (PDJSs), where the evolution of the continuous state in each mode is modeled by a deterministic differential equation and transitions between modes are governed by a continuous-time Markov process [5,13,16,17,50]. In general, the transitions rates in PDJs are assumed independent of the continuous state, which is too restrictive for our applications.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Hybrid Systems: Application to Communication Networks

Hespanha

2004

Lecture Notes in Computer Science

134

122

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Abstract. We propose a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for Piecewise-Deterministic Markov Process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state. As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model. This model shows that, for transfer-size distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.

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Section: Introductionmentioning

confidence: 99%

Stochastic Hybrid Systems: Application to Communication Networks

Hespanha

2004

Lecture Notes in Computer Science

134

122

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“…This together with (4) yields that A T cliP 1i A cli −P 1i < 0, which implies that the system in (2) is stochastically stable (Costa & Fragoso, 1993;Ji et al, 1991).…”

Section: Preliminariesmentioning

confidence: 92%

“…This is partially due to their widespread applications to modeling various practical processes that experience abrupt changes in their structure and parameters, possibly caused by phenomena such as component failures or repairs, sudden environmental disturbances, and changing subsystem interconnections. Stability of DMJLSs has been investigated thoroughly in Costa and Fragoso (1993), and the equivalence of different second moment stability has been established in Ji, Chizeck, Feng, and Loparo (1991). The linear quadratic optimal control problem for DMJLSs has been studied in Chizeck, Willsky, and Castanon (1986) and Costa and de Paulo (2007), and the filtering problem has been considered in Costa and Marques (2000).…”

Section: Introductionmentioning

confidence: 99%

Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

2010

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a b s t r a c tThis paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical examples.

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“…Defining ( ) = inf ≥ ( + ), then we get At the same time, ( ) → ( → ∞) exponentially fast. From (37), as → ∞, we obtain the mean state covariance as follows:…”

Section: Assumption 8 System (1) Is Mean Square Stable (Mss)mentioning

confidence: 99%

“…In order to solve the optimal estimation problem, the measurements' loss process is modeled as a Bernoulli distributed white sequence taking values from 0 to 1 randomly. The estimation problem is then reformulated as an optimal linear filtering of a class of MJLSs, which have random missing observation and necessary model compensation, via state augmentation [35][36][37][38]. A recursive filtering is formulated in terms of Riccati difference equations.…”

Section: Introductionmentioning

confidence: 99%

Optimal State Estimation for Discrete-Time Markov Jump Systems with Missing Observations

Sun

Zhao

Yin

2014

Abstract and Applied Analysis

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This paper is concerned with the optimal linear estimation for a class of direct-time Markov jump systems with missing observations. An observer-based approach of fault detection and isolation (FDI) is investigated as a detection mechanic of fault case. For systems with known information, a conditional prediction of observations is applied and fault observations are replaced and isolated; then, an FDI linear minimum mean square error estimation (LMMSE) can be developed by comprehensive utilizing of the correct information offered by systems. A recursive equation of filtering based on the geometric arguments can be obtained. Meanwhile, a stability of the state estimator will be guaranteed under appropriate assumption.

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Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters

Cited by 510 publications

References 0 publications

Stochastic Hybrid Systems: Application to Communication Networks

Stochastic Hybrid Systems: Application to Communication Networks

Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

Optimal State Estimation for Discrete-Time Markov Jump Systems with Missing Observations

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