scholarly journals Stabilization of Discrete-Time Markovian Jump Systems via Controllers with Partially Mode-Dependent Characterization

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chunyan Zhai ◽  
Dingyu Xue ◽  
Shuchen Li ◽  
Guoliang Wang
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Packet Dropout ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stabilizing Controller ◽  
Unreliable Networks ◽  
Jump Systems

A kind of stabilizing controller in terms of being partially mode-dependent is developed for discrete-time Markovian jump systems (MJSs). The property referred to be partially mode-dependent is described by the Bernoulli variable. Based on the established model, the stabilization for MJSs over unreliable networks is considered, where both network-induced delay and packet dropout take place in system modes and states. Such effects of network are taken into account in controller design. All the conditions are derived in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and applicability of the proposed method.

Disturbance-observer-based l2–l∞ control for discrete-time Markovian jump system

2018 ◽  
Vol 40 (9) ◽  
pp. 2807-2812 ◽  
Author(s):  
Linlin Hou ◽  
Haibin Sun
Keyword(s):  
Discrete Time ◽  
Disturbance Observer ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
First Case ◽  
Control Scheme ◽  
Jump Systems

This paper considers the problem of anti-disturbance control for discrete-time Markovian jump systems with multiple disturbances. The controller is constructed via disturbance-observer-based control and l2– l∞ control. The disturbances are divided into two parts. One, in the same channel as the control inputs, is described by an exogenous system. The other is assumed to be bounded with an [Formula: see text] norm. A disturbance observer is presented to estimate and reject the first-case disturbances for discrete-time Markovian jump systems, and an l2– l∞ control scheme is used to attenuate the second-case disturbances. By using linear matrix inequalities, a solvable sufficient condition is developed. Finally, the effectiveness of the proposed control scheme is demonstrated via a numerical example.

scholarly journals Robust Stabilization of Stochastic Markovian Jump Systems with Distributed Delays

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Guilei Chen ◽  
Zhenwei Zhang ◽  
Chao Li ◽  
Dianju Qiao ◽  
Bo Sun
Keyword(s):  
Linear Matrix Inequalities ◽  
Robust Stabilization ◽  
Distributed Delays ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Parameter Uncertainties ◽  
Delay Dependent ◽  
Jump Systems

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory.

scholarly journals Finite-Time Stabilization for Discrete-Time Delayed Markovian Jump Systems with Partially Delayed Actuator Saturation

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Guoliang Wang ◽  
Bo Feng
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Controller Design ◽  
Actuator Saturation ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Time Control ◽  
Jump Systems

The finite-time control problem of discrete-time delayed Markovian jump systems with partially delayed actuator saturation is considered by a mode-dependent parameter approach. Different from the traditionally saturated actuators, a kind of saturated actuator being partially delay-dependent is firstly proposed, where both nondelay and delay states are included and occur asynchronously. Moreover, the probability distributions of such two terms are described by the Bernoulli variable and are taken into account in the controller design. Sufficient conditions for the existence of the desired controller are presented with LMIs. Finally, a numerical example is provided to show the effectiveness and superiority of the obtained results.

scholarly journals On Delay-Range-Dependent Stochastic Stability Conditions of Uncertain Neutral Delay Markovian Jump Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xinghua Liu ◽  
Hongsheng Xi
Keyword(s):  
Stochastic Stability ◽  
Convex Combination ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Neutral Delay ◽  
Jump Systems

The delay-range-dependent stochastic stability for uncertain neutral Markovian jump systems with interval time-varying delays is studied in this paper. The uncertainties under consideration are assumed to be time varying but norm bounded. To begin with the nominal systems, a novel augmented Lyapunov functional which contains some triple-integral terms is introduced. Then, by employing some integral inequalities and the nature of convex combination, some less conservative stochastic stability conditions are presented in terms of linear matrix inequalities without introducing any free-weighting matrices. Finally, numerical examples are provided to demonstrate the effectiveness and to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

scholarly journals H∞Control of Singular Markovian Jump Systems with Bounded Transition Probabilities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongsheng Lin ◽  
Ying Li ◽  
Guoliang Wang
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Disturbance Attenuation ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Singular Markovian Jump Systems ◽  
Jump Systems

This paper discussesH∞control problems of continuous-time and discrete-time singular Markovian jump systems (SMJSs) with bounded transition probabilities. Improved sufficient conditions for continuous-time SMJSs to be regular, impulse free, and stochastically stable withγ-disturbance attenuation are established via less conservative inequality to estimate the transition jump rates, so are the discrete-time SMJSs. With the obtained conditions, the design of a state feedback controller which ensures the resulting closed-loop system to be stochastically admissible and withH∞performance is given in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are presented to show the effectiveness and the benefits of the proposed approaches.

A diffusive representation approach toward H∞ sliding mode control design for fractional-order Markovian jump systems

2020 ◽  
pp. 095965182097525
Author(s):  
Majid Parvizian ◽  
Khosro Khandani
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Markovian Jump Systems ◽  
Markovian Jump ◽  
Suggested Approach ◽  
Stabilizing Controller ◽  
Mode Control ◽  
Jump Systems ◽  
Diffusive Representation

This article proposes a new [Formula: see text] sliding mode control strategy for stabilizing controller design for fractional-order Markovian jump systems. The suggested approach is based on the diffusive representation of fractional-order Markovian jump systems which transforms the fractional-order system into an integer-order one. Using a new Lyapunov–Krasovskii functional, the problem of [Formula: see text] sliding mode control of uncertain fractional-order Markovian jump systems with exogenous noise is investigated. We propose a sliding surface and prove its reachability. Moreover, the linear matrix inequality conditions for stochastic stability of the resultant sliding motion with a given [Formula: see text] disturbance attenuation level are derived. Eventually, the theoretical results are verified through a simulation example.

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