An LMI approach to stabilization of linear discrete-time periodic systems

Souza, Carlos E. de; Trofino, Alexandre

doi:10.1080/002071700403466

Cited by 110 publications

(65 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worthwhile to note that the matrix inequalities in Theorems 2.1-2.2, Lemma 3.1, and Theorems 3.1-3.2 can be transformed to linear matrix inequalities (LMI) by using the result (Theorem 3) in [44], thus can be also solved by existing optimization techniques proposed by Boyd et al [45].…”

Section: Remark 32mentioning

confidence: 99%

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

Shi

Boukas

Nguang

et al. 2003

Optim Control Appl Methods

View full text Add to dashboard Cite

SUMMARYThe problems of stochastic stability and stochastic disturbance attenuation for a class of linear discretetime systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique.

show abstract

Section: Remark 32mentioning

confidence: 99%

Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

Shi

Boukas

Nguang

et al. 2003

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

“…The proposed numerical application is a fractional version of an example proposed in [17]. Studied system is described by representation (7) where:…”

Section: Numerical Examplementioning

confidence: 99%

Fractional order polytopic systems: robust stability and stabilisation

2011

View full text Add to dashboard Cite

This article addresses the problem of robust pseudo state feedback stabilisation of commensurate fractional order polytopic systems (FOS). In the proposed approach, Linear Matrix Inequalities (LMI) formalism is used to check if the pseudo-state matrix eigenvalues belong to the FOS stability domain whatever the value of the uncertain parameters. The article focuses particularly on the case of a fractional order ν such that 0 < ν < 1, as the stability region is non-convex and associated LMI condition is not as straightforward to obtain as in the case 1 < ν < 2. In relation to the quadratic stabilisation problem previously addressed by the authors and that involves a single matrix to prove stability of the closed loop system, additional variables are then introduced to decouple system matrices in the closed loop system stability condition. This decoupling allows using parameter-dependent stability matrices and leads to less conservative results as attested by a numerical example.

show abstract

“…For most of the available controller synthesis methods for periodic systems, existence of a periodically time-varying LF for the closed-loop dynamics can be derived, either directly or by the converse result in Jiang and Wang (2002). Consider methods based on the periodic Riccati equation Bittanti et al (1991), Varga (2008), output feedback schemes De Souza and Trofino (2000), H 2 synthesis for the case of linear periodic systems with polytopic uncertainties Farges et al (2007), eigenvalue assignment Brunovský (1970), Kabamba (1986) Email addresses: n.athanasopoulos@tue.nl (Nikolaos Athanasopoulos), m.lazar@tue.nl (Mircea Lazar), christoph.boehm@hilti.com (Christoph Böhm), frank.allgower@ist.uni-stuttgart.de (Frank Allgöwer).…”

Section: Introductionmentioning

confidence: 99%