Static Output Feedback Stabilization: An ILMI Approach

Cao, Yong‐Yan; Lam, James; Sun, You-Xiam

doi:10.1016/s0005-1098(98)80021-6

Cited by 521 publications

(313 citation statements)

References 17 publications

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“…By solving the optimization problem P s with the system matrices A, B u and B w given in (19) and (20), the matrices C z and D z defined in (22), and the value…”

Section: Structure Modelmentioning

confidence: 99%

“…In this case, however, it should be highlighted that obtaining an optimal matrix K can involve serious computational difficulties [17][18][19][20]. According to the design method presented in [21], a suboptimal gain matrix K can be effectively computed by considering the state-feedback LMI optimization problem P s in (31) and the following transformations of the LMI variables X and Y:…”

Section: H ∞ Controller With Neighbouring State Informationmentioning

confidence: 99%

“…Even for a moderate number of stories, a rich variety of control setups can be obtained in this case, and designs with different degrees of complexity can be considered for a given control problem. The potential benefits provided by this broader approach, however, are seriously compromised by the challenging theoretical and computational issues associated to the design of optimal controllers with partial state information [17][18][19][20].…”

mentioning

confidence: 99%

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Vibration control strategy for large‐scale structures with incomplete multi‐actuator system and neighbouring state information

nonero¹,

Massegú²,

Rossell³

et al. 2016

IET Control Theory & Applications

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The synthesis of optimal controllers for vibrational protection of large-scale structures with multiple actuation devices and partial state information is a challenging problem. In this paper, we present a design strategy that allows computing this kind of controllers by using standard linear matrix inequality optimization tools. To illustrate the main elements of the new approach, a five-story structure equipped with two interstory actuation devices and subjected to a seismic disturbance is considered. For this control setup, three different controllers are designed: an ideal state-feedback H ∞ controller with full access to the complete state information and two static output-feedback H ∞ controllers with restricted neighbouring state information. To assess the performance of the proposed controllers, the corresponding frequency responses are investigated and a proper set of numerical simulations are conducted, using the full scale North-South El Centro 1940 seismic record as ground acceleration input. The obtained results indicate that, despite the severe information constraints, the proposed static output-feedback controllers attain a level of seismic protection that is very similar to that achieved by the ideal state-feedback controller with complete state information.

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“…By solving the optimization problem P s with the system matrices A, B u and B w given in (19) and (20), the matrices C z and D z defined in (22), and the value…”

Section: Structure Modelmentioning

confidence: 99%

Section: H ∞ Controller With Neighbouring State Informationmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Vibration control strategy for large‐scale structures with incomplete multi‐actuator system and neighbouring state information

nonero¹,

Massegú²,

Rossell³

et al. 2016

IET Control Theory & Applications

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“…If no such matrices are found, we can conclude immediately that the system is not SOF stabilizable. Like many other iterative algorithms (Cao, Lam, & Sun, 1998;Cao, Sun, & Mao, 1998;Fujimori, 2004;Gadewadikar, Lewis, Xie, Kucera, & Abu-Khalaf, 2007;Iwasaki, 1999), the sequence of iterates depends on the selection of initial values, and appropriate selection of M (1) i will improve the solvability. In addition, it should be emphasized that the tuning parameter α may affect the optimum of the converged value γ (∞) * , although larger α make the condition less stringent.…”

Section: Remark 7 the Initial Values M (1)mentioning

confidence: 99%

Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

2010

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a b s t r a c tThis paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical examples.

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“…ILMI Iterative Linear Matrix Inequality [16]: a partir de un valor inicial establecido heurísticamente para alguna de las variables de decisión (las mínimas necesarias para que el problema sea LMI), iterar sustituyendo de forma alternada en cada iteración hasta una cierta condición de parada o no factibilidad. Este método es quizá el más simple pero existe una fuerte dependencia del valor inicial y por ende, no garantiza la obtención de una soluciónóptima (o ni siquiera factible, aunque exista).…”

Section: Realimentación Estática Del Estadounclassified

Controladores digitales basados en predictor para sistemas con retardos variables en el tiempo

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Static Output Feedback Stabilization: An ILMI Approach

Cited by 521 publications

References 17 publications

Vibration control strategy for large‐scale structures with incomplete multi‐actuator system and neighbouring state information

Vibration control strategy for large‐scale structures with incomplete multi‐actuator system and neighbouring state information

Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

Controladores digitales basados en predictor para sistemas con retardos variables en el tiempo

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