On the exponential stability of stochastic Markovian jump systems

This paper deals with the exponential stability of the class of stochastic systems with jumps. For the linear case, a sufficient condition, which guarantees that the nominal system with a bounded diffusion term remains stable under a state feedback control law, is established. For the case of uncertain linear stochastic system, we have designed an optimal control law that guarantees the robust exponential stability of the systems. Finally, for the nonlinear case with matching conditions, we have established a similar result.published_or_final_versio

Analysis and synthesis of Markov Jump Linear systems with time-varying delays and partially known transition probabilities

In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory. © 2008 IEEE.published_or_final_versio

A delay-dependent approach to H∞ filtering for stochastic delayed jumping systems with sensor non-linearities

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Taylor & Francis Ltd.In this paper, a delay-dependent approach is developed to deal with the stochastic H∞ filtering problem for a class of It type stochastic time-delay jumping systems subject to both the sensor non-linearities and the exogenous non-linear disturbances. The time delays enter into the system states, the sensor non-linearities and the external non-linear disturbances. The purpose of the addressed filtering problem is to seek an H∞ filter such that, in the simultaneous presence of non-linear disturbances, sensor non-linearity as well as Markovian jumping parameters, the filtering error dynamics for the stochastic time-delay system is stochastically stable with a guaranteed disturbance rejection attenuation level γ. By using It's differential formula and the Lyapunov stability theory, we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist. These conditions are dependent on the length of the time delay. We then characterize the expression of the filter parameters, and use a simulation example to demonstrate the effectiveness of the proposed results.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Nuffield Foundation of the U.K.under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Optimal Tracker For Unreliable Manufacturing Systems

This paper deals with the inventory-production control problem where the produced items are assumed to deteriorate at a rate that depends on the demand rate of the production system. The state of this production system is assumed to be described by a continuous-time Markov process taking values in a finite discrete space. The inventory-production control problem is formulated as a stochastic optimal control problem. The optimal policy that solves the optimal control problem is obtained in terms of a set of coupled Riccati equations. The guaranteed cost problem is also treated. A numerical example is provided to show the usefulness of the proposed model

Guaranteed Cost Control Of A Markov Jump Linear Uncertain System Using A Time-Multiplied Cost Function

This paper addresses the guaranteed cost control problem of jump linear systems with norm-bounded uncertain parameters. A time-multiplied performance index is considered. The performance is calculated first and an LMI-based algorithm is developed to design a state feedback control law with constant gain matrices which robustly stabilizes the system in the mean-square quadratically stable sense

Guaranteed Cost Control Of A Markov Jump Linear Uncertain System Using A Time-Multiplied Cost Function

This paper addresses the guaranteed cost control problem of jump linear systems with norm-bounded uncertain parameters. A time-multiplied performance index is considered. The performance is calculated first and an LMI-based algorithm is developed to design a state feedback control law with constant gain matrices which robustly stabilizes the system in the mean-square quadratically stable sense

Guaranteed Cost Control Of A Markov Jump Linear Uncertain System Using A Time-Multiplied Cost Function

This paper addresses the guaranteed cost control problem of jump linear systems with norm-bounded uncertain parameters. A time-multiplied performance index is considered. The performance is calculated first and an LMI-based algorithm is developed to design a state feedback control law with constant gain matrices which robustly stabilizes the system in the mean-square quadratically stable sense

Guaranteed Cost Control Of A Markov Jump Linear Uncertain System UsingA Time-Multiplied Cost Function

This paper addresses the guaranteed cost control problem of jump linear systems with norm-bounded uncertain parameters. A time-multiplied performance index is considered. The performance is calculated first and an LMI-based algorithm is developed to design a state feedback control law with constant gain matrices which robustly stabilizes the system in the mean-square quadratically stable sense

Robust Inventory-Production Control Problem With Stochastic Demand

This paper deals with the inventory-production control problem where the produced items are supposed to be deteriorating with a rate that depends on the stochastic demand rate. The inventory-production control problem is formulated as a jump linear quadratic control problem. The optimal policy that solves the optimal control problem is obtained in terms of a set of coupled Riccati equations. The guaranteed cost control problem is also investigated. Copyright (C) 1999 John Wiley Sons, Ltd