ℋ2 and ℋ∞ε-guaranteed cost computation of uncertain linear systems

Gonçalves, Eduardo Nunes; Palhares, Reinaldo M.; Takahashi, Ricardo H. C.; Mesquita, Renato C.

doi:10.1049/iet-cta:20050334

Cited by 21 publications

(11 citation statements)

References 14 publications

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“…In order to verify the controller computed in the first step, in the second step an analysis procedure based on a combination of a branch-and-bound algorithm and LMI formulations is applied (Gonc¸alves, Palhares Takahashi, and Mesquita 2007). This analysis procedure is capable of finding the coordinates 2 of the maximum values of kEk 1 , kT cd k 1 and kT un k 2 , if the closed-loop system is robustly stable, or a coordinate 2 of an unstable system, if the system is not robustly stable.…”

Section: Multi-objective Robust Control Synthesis Proceduresmentioning

confidence: 99%

“…This algorithm ends when the difference between the bounding functions is smaller than the prescribed relative accuracy. The algorithm is implemented considering as lower bound function the maximum H 1 (or H 2 )-norm computed in the vertices and as upper bound function the worst case of H 1 (or H 2 ) guaranteed cost computed by means of LMI formulations, both functions calculated for subdivisions of the original polytope (Gonc¸alves et al 2007). In this article, for continuous-time systems, the guaranteed cost computations are based on: Lemma 1 presented in de Oliveira, Oliveira, Leite, Montagner, and Peres (2004a) for H 1 guaranteed cost and combination of Lemmas 1 and 2 presented in de Oliveira, Oliveira, Leite, Montagner, and Peres (2004b) for H 2 guaranteed cost.…”

Section: Multi-objective Robust Control Synthesis Proceduresmentioning

confidence: 99%

See 1 more Smart Citation

Robust ℋ₂/ℋ_∞/reference model dynamic output-feedback control synthesis

Gonçalves

Bachur

Palhares

et al. 2011

International Journal of Control

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This article presents a new strategy to design robust model matching dynamic output-feedback controllers that guarantee tracking response specifications, disturbance rejection and noise attenuation. The proposed synthesis methodology, based on a multi-objective optimisation problem, can be applied to uncertain continuous or discrete-time linear time-invariant systems with polytopic uncertainty, leading to both full-order and reducedorder robust-performance dynamic controllers. The objective functions represent the H 1 -norm of the difference between the closed-loop transfer function matrix, from the reference signals and the plant outputs and the reference model matrix, the H 1 -norm of the closed-loop transfer function matrix from the disturbances and the plant outputs and the H 2 -norm of the closed-loop transfer function matrix from the measurement noises and the control inputs. An integral control action is also introduced in order to achieve zero steady-state error. In the case of MIMO systems, the proposed strategy can be applied to decouple the closed-loop control system choosing an appropriated reference model matrix. Two examples are presented to illustrate both SISO and MIMO systems control synthesis.

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Section: Multi-objective Robust Control Synthesis Proceduresmentioning

confidence: 99%

Section: Multi-objective Robust Control Synthesis Proceduresmentioning

confidence: 99%

Robust ℋ₂/ℋ_∞/reference model dynamic output-feedback control synthesis

Gonçalves

Bachur

Palhares

et al. 2011

International Journal of Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let (19) According to the Lemma 4, it is equivalent that there exists a positive scalar ES > 0 satisfying…”

Section: B Regional Pole Assignment Conditionmentioning

confidence: 99%

“…As pointed in [13] that LMI is a powerful formulation for a wide variety of control problems. With the presence of the interior point algorithm of the convex Optimization [14][15][16][17], the LMls technique has been applied in more and more fields [18][19][20][21][22][23]. In addition, solving the LMI problems are available on commercial software, such as MATLAB, so the analysis and design problems formulated by LMls can be efficiently solved.…”

mentioning

confidence: 99%

Robust control of norm-bounded uncertain linear system with regional pole assignment

2009

2009 International Conference on Mechatronics and Automation

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This paper proposes a robust controller design method for an norm-bounded uncertain linear system with disturbance. At First, we derive the necessary and sufficient condition for regional pole assignment for uncertain linear system, then derive the criteria of H 2/H oo performance of uncertain linear system with disturbance. Hence combining them, we get the mixed H 2/H oo controller control with regional assignment for norm-bounded uncertain linear system with disturbance. The problem of the robust controller designed is changed into an optimization problem, and the robust controller is parameterized by the solution of the optimization. Since the optimization problem conditions are expressed in term of linear matrix inequalities, so it makes the proposed method practical utility. Finally the numerical example illustrates the effectiveness of the proposed approach.

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“…For this controller, and considering the whole polytope, [18] presents the following values for the H 2 and H 1 norms computed via a different approach described in [22,21]:…”

Section: Norm Computation For Uncertain Systemsmentioning

confidence: 99%