Delay-dependent and decay-rate-dependent conditions for exponential mean stability and non-fragile controller design of positive Markov jump linear systems with time-delay

Abstract This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

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Receding Horizon Control for Uncertain Markov Jump Linear Systems with Time Delay and Actuator Saturation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.303-306.1193 ◽

2013 ◽

Vol 303-306 ◽

pp. 1193-1199 ◽

Cited By ~ 3

Author(s):

Ji Wei Wen

Keyword(s):

Time Delay ◽

Linear Systems ◽

Actuator Saturation ◽

Receding Horizon Control ◽

Receding Horizon ◽

Markov Jump ◽

Jump Linear Systems ◽

Current Time ◽

Mean Square Stability ◽

Markov Jump Linear Systems

A robust receding horizon control (RHC) scheme is developed for uncertain discrete-time Markov Jump Linear Systems (MJLS) with time delay and actuator saturation where the system uncertainties and jumping transition probabilities are assumed to belong to some convex sets. Firstly, when time delay is considered, a sufficient condition of minimizing upper bound of the cost function and mean square stability of the closed-loop system are established based on the Lyapunov Krasovskii function which depend on the current time jump mode. At each sampling time, an optimal control gain can be obtained by solving the semi-definite programming (SDP) problem. Then, the proposed strategy is extended to design robust RHC scheme for uncertain MJLS with both time delay and actuator saturation. Moreover, the domain of attraction can be estimated through a modified invariant ellipsoid. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

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Stochastic finite-time stabilization of discrete-time positive Markov jump linear systems with time-delay

2016 35th Chinese Control Conference (CCC) ◽

10.1109/chicc.2016.7553328 ◽

2016 ◽

Author(s):

Lang Ma ◽

Shuqian Zhu ◽

You Xu ◽

Bo Wang

Keyword(s):

Time Delay ◽

Linear Systems ◽

Discrete Time ◽

Finite Time ◽

Markov Jump ◽

Jump Linear Systems ◽

Markov Jump Linear Systems ◽

Finite Time Stabilization

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H∞ State-Feedback Control for Semi-Markov Jump Linear Systems With Time-Varying Delays

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4024009 ◽

2013 ◽

Vol 135 (4) ◽

Cited By ~ 29

Author(s):

Ji Huang ◽

Yang Shi

Keyword(s):

Linear Systems ◽

State Feedback ◽

Controller Design ◽

State Feedback Control ◽

Linear Matrix ◽

Sufficient Condition ◽

Time Varying ◽

Markov Jump ◽

Jump Linear Systems ◽

Markov Jump Linear Systems

Semi-Markov jump linear systems (S-MJLSs) are more general than Markov jump linear systems in modeling practical systems. This paper investigates the H∞ control problem for a class of semi-Markov jump linear systems with time-varying delays. The sojourn-time partition technique is firstly proposed for the delayed stochastic switching system. A sufficient condition for designing the state feedback controller is then established. Moreover, the sufficient condition is expressed as a set of linear matrix inequalities which can be readily solved. A numerical example illustrates the effectiveness of the proposed controller design technique.

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