H∞ State Feedback Control of Discrete-time Markov Jump Linear Systems through Linear Matrix Inequalities*

Gonçalves, Alim P. C.; Fioravanti, André R.; Al-Radhawi, M. Ali; Geromel, J.C.

doi:10.3182/20110828-6-it-1002.02548

Cited by 11 publications

(25 citation statements)

References 18 publications

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“…(17), as detailed in [17]. The next corollary, already reported in [18], compares our results with that of Theorem 3.4 from [27]. Proof.…”

Section: Uncertain Probabilitiessupporting

confidence: 53%

“…Proof. The proof follows the same pattern already shown in [18] by showing that for g40 given, the feasibility of LMIs of Theorem 3.4 from [27] implies the feasibility of LMIs (8) and (9) at the vertices of the polytope (17). Since those sets of LMIs are affine with respect to the transition probabilities, the minimum g is an upper bound for the closed loop H 1 norm.…”

Section: Uncertain Probabilitiesmentioning

confidence: 66%

See 1 more Smart Citation

H∞ robust and networked control of discrete-time MJLS through LMIs

Gonçalves

Fioravanti

Geromel

2012

Journal of the Franklin Institute

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“…(17), as detailed in [17]. The next corollary, already reported in [18], compares our results with that of Theorem 3.4 from [27]. Proof.…”

Section: Uncertain Probabilitiessupporting

confidence: 53%

Section: Uncertain Probabilitiesmentioning

confidence: 66%

H∞ robust and networked control of discrete-time MJLS through LMIs

Gonçalves

Fioravanti

Geromel

2012

Journal of the Franklin Institute

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“…In contrast, little work has been done with incomplete mode information of the system regardless of its significance in practical MJLSs. Concerning partial or local mode information, two representative methods have been developed in the literature, i.e., local observations of the system operation modes [13], [14] and cluster observations of the system operation modes [5], [8], [9]. In the first one, the system is firstly decomposed into a set of interconnected lower dimensional subsystems, and local decentralized controllers are then designed based only on the state and mode information locally available within the subsystems; while in the second one, the complete Markov modes are firstly split into several non-overlapping clusters.…”

Section: Introductionmentioning

confidence: 99%

“…Unlike some existing controllers proposed in [13], [14], we not only use full state information and local mode information, but also take the knowledge of group modes of the reformulated system into consideration. Different from [5], [8], [9], we allow overlapping operation modes to be existed in the formed groups. Moreover, the jumps among different groups are governed by the high-level Markov chain.…”

Section: Introductionmentioning

confidence: 99%

Overlapping mode-dependent H<inf>∞</inf> control of discrete-time Markovian jump linear systems

Han

Jiang

2013

52nd IEEE Conference on Decision and Control

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This paper is concerned with overlapping modedependent H∞ control for a discrete-time Markov jump linear system in the presence of overlapping local operation modes and incomplete mode transition probabilities. By developing a randomly overlapping decomposition method, the system with deficient global operation modes is reformulated by a set of locally overlapping switched groups with accessible group and local modes. An overlapping group-and local-mode-dependent state feedback controller is delicately constructed. Unlike some existing controllers proposed in the literature, we do not require complete global mode information, but take full advantage of the knowledge of group and local modes of the reformulated system. Moreover, overlapping local modes are allowed to be existed in the formed groups. The stability analysis and control design procedures are developed based on the stochastic Lyapunov functional approach. The proposed framework is shown to be more general, which covers the traditional Markovian jump linear system with completely available global modes as a special case. In the case of only one local group, it is also shown that some existing results from the literature can be regarded as a special case of our derived results. A simulation example is finally presented to show the effectiveness and merits of the proposed method.

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“…However, similar analysis tools can be used. Some examples are the recent survey paper [156] and other references such as [142,148,149,162,164,168]. Because of the formality and completeness of the analysis, the paper [135] and the book [134] of the same authors deserve special attention.…”

Section: Stability Of Switched Systemsmentioning

confidence: 99%

Consensus in Multi‐agent Systems

Wen

Chen

et al. 2016

Distributed Cooperative Control of Multi‐agent Systems

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A Carlos Elías y a Marina. AbstractDuring the last decade, the problem of consensus in multiagents systems has been studied with special emphasis on graph theoretical methods. Consensus can be regarded as a control objective in which is sought that all systems, or agents, in a network have an equivalent output value. This is achieved through a given control strategy usually referred to as consensus algorithm. The motivation to study such an objective comes from different areas, such as engineering, and social and natural sciences. In the control engineering field, important application examples are formation control of swarms of mobile robots and distributed electric generation. Most of the work in this area is done for agents with single or double integrator dynamics and algorithms derived as the Laplacian matrix of undirected graphs. That is, consensus is often studied as a property of particular networks and particular algorithms.In this thesis, we tackle the problem from a Control Theory perspective in an attempt to augment the class of systems that can be studied. For that we translate the consensus problem from its classical formulation for integrator systems into a general continuous time stability problem. From here, different algorithmic strategies under several dynamical assumptions of the agents can be studied through well known control theoretical tools -as Lyapunov's theory, linear matrix inequalities (LMI), or robust control -along with graph theoretical concepts. In particular, in this work we study consensus of agents with arbitrary linear dynamics under the influence of linear algorithms not necessarily derived from graphs. Furthermore, we include the possibility that the agents are disturbed by several factors as external signals, parameter uncertainties, switching dynamics, or communication failure. The theoretical analysis is also applied to the problem of power sharing in electric grids and to the analysis of distributed formation control.

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H∞ State Feedback Control of Discrete-time Markov Jump Linear Systems through Linear Matrix Inequalities*

Cited by 11 publications

References 18 publications

H∞ robust and networked control of discrete-time MJLS through LMIs

H∞ robust and networked control of discrete-time MJLS through LMIs

Overlapping mode-dependent H<inf>∞</inf> control of discrete-time Markovian jump linear systems

Consensus in Multi‐agent Systems

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H∞ State Feedback Control of Discrete-time Markov Jump Linear Systems through Linear Matrix Inequalities*

Cited by 11 publications

References 18 publications

H∞ robust and networked control of discrete-time MJLS through LMIs

H∞ robust and networked control of discrete-time MJLS through LMIs

Overlapping mode-dependent H<inf>&#x221E;</inf> control of discrete-time Markovian jump linear systems

Consensus in Multi‐agent Systems

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Overlapping mode-dependent H<inf>∞</inf> control of discrete-time Markovian jump linear systems