Guaranteed cost control for bilinear systems by static output feedback

Kang, Dongyeop; Won, Sangchul; Jang, Yu Jin

doi:10.1016/j.amc.2012.12.086

Cited by 7 publications

(7 citation statements)

References 37 publications

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“…It is straight forward to extend (11) to the case with non-zero references for states and inputs. However, inclusion of non-zero references may raise additional questions about the admissibility of the references with regards to the system dynamics.…”

Section: Direct Optimal Controller Designmentioning

confidence: 99%

“…In [10] a general framework for analyzing nonlinear systems is discussed by using SOS programming method. There are also a few of papers proposing SOS programming for control of continuous time bilinear systems, see, e.g., [11], [12] and references therein. In [6] it is stated that 'It is not surprising that very few works dealing with the stabilization problem of discrete-time systems have been reported.…”

Section: Introductionmentioning

confidence: 99%

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Control design and analysis for discrete time bilinear systems using Sum of Squares methods

Vatani

Hovd

Olaru

2014

53rd IEEE Conference on Decision and Control

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Abstract-In this paper, stabilization of discrete time bilinear systems is investigated by using Sum of Squares (SOS) programming methods and a quadratic Lyapunov function. Starting from the fact that global asymptotic stability cannot be proven with a quadratic Lyapunov function if the controller is polynomial in the states, the controller is instead proposed to be a ratio of two polynomials of the states. First, a simple one-step optimal controller is designed, and it is found that it is indeed defined as a ratio of two polynomials. However, this simple controller design does not result in any stability guarantees. For stability investigation, the Lyapunov difference inequality is converted to a SOS problem, and an optimization problem is proposed to design a controller which maximizes the region of convergence of the bilinear system. Input constraints can also be accounted for in the optimization problem.

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Section: Direct Optimal Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Control design and analysis for discrete time bilinear systems using Sum of Squares methods

Vatani

Hovd

Olaru

2014

53rd IEEE Conference on Decision and Control

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“…The corresponding controller in (11) is C.x.k// D K; K c 0 .x.k// D 0. P tX=trace.X /, with a constant t > 0 2 Maximize with the parameters of s 1 .x;´/ and q i .x/ as free variables, subject to constraints (12) and (15), s 1 .x;´/; q i .x/ SOS. Equations (12) and (15) contain bilinear terms in , s 1 .x;´/ and q i .x/, and the maximization is therefore performed iteratively by verifying the constraints for increasing values of .…”

Section: Algorithm 1: Controller Design Proceduresmentioning

confidence: 99%

“…A representative overview of these works is beyond the scope of this paper, but some inspiration from Gutman is acknowledged. Closer to the topic of interest of the current paper, controller design using SOS programming for continuous time bilinear systems has previously been addressed in . There are fewer references on discrete‐time bilinear systems.…”

Section: Introductionmentioning

confidence: 99%

Control design for discrete‐time bilinear systems using the scalarized Schur complement

Vatani

Hovd

Olaru

2017

Intl J Robust & Nonlinear

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Summary In this paper, controller design for discrete‐time bilinear systems is investigated by using sum of squares programming methods and quadratic Lyapunov functions. The class of rational polynomial controllers is considered, and necessary conditions on the degree of controller polynomials for quadratic stability are derived. Next, a scalarized version of the Schur complement is proposed. For controller design, the Lyapunov difference inequality is converted to a sum of squares problem, and an optimization problem is proposed to design a controller, which maximizes the region of quadratic stability of the bilinear system. Input constraints can also be accounted for. Copyright © 2017 John Wiley & Sons, Ltd.

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“…The concept of guaranteed cost control is proposed to make the closed‐loop system asymptotically stable and also guarantee an adequate level performance of a system. The problem under consideration has the advantage of providing an upper bound on performance index of a system . The degradation of system performance incurred by input constraints is improved, and the acceptable time delay value less than an upper bound is guaranteed.…”

Section: Introductionmentioning

confidence: 99%

Robust reliable guaranteed cost control for uncertain T‐S fuzzy neutral systems with interval time‐varying delay and linear fractional perturbations

Lien

Chang

et al. 2014

Optim Control Appl Methods

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SummaryThe robust reliable guaranteed cost control for Takagi–Sugeno fuzzy systems with interval time‐varying delay is considered in this paper. Some free weighting matrices and non‐negative terms are provided to improve the conservativeness of our main results. An LMI optimization approach is applied to solve the problems of robust reliable guaranteed cost control and minimization of cost function. Copyright © 2014 John Wiley & Sons, Ltd.

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Guaranteed cost control for bilinear systems by static output feedback

Cited by 7 publications

References 37 publications

Control design and analysis for discrete time bilinear systems using Sum of Squares methods

Control design and analysis for discrete time bilinear systems using Sum of Squares methods

Control design for discrete‐time bilinear systems using the scalarized Schur complement

Robust reliable guaranteed cost control for uncertain T‐S fuzzy neutral systems with interval time‐varying delay and linear fractional perturbations

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