Regional stabilization of rational discrete-time systems with magnitude control constraints

Oliveira, M. Z.; Silva, J. M. Gomes da; Coutinho, Daniel

doi:10.1109/acc.2013.6579844

Cited by 4 publications

(12 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Consider a single-input bilinear discrete-time system of the form (7) and a rational polynomial controller (4). The closed loop system is globally quadratic stable only if any state Q x j representing an endogenously bilinear mode has the same maximal degree in the numerator and denominator polynomial of the rational polynomial controller.…”

Section: Propositionmentioning

confidence: 99%

“…Substitute in the plant dynamics (7), the controller (4), and multiply with Q For point (2), evaluate the controller for Q x D Q x 1 v T T for any finite, constant vector v, and let Q…”

Section: Proofmentioning

confidence: 99%

“…Use of SOS programming for the design of polynomial controllers for polynomial continuous-time systems is studied in [4] and [5], while works on nonlinear discrete-time systems include, for example, [6,7]. In [7], the use of linear state feedback is studied, whereas [6] addresses the synthesis of polynomial controllers, taking input saturation into account. This paper considers SOS-based controller design for discrete-time bilinear systems using rational polynomial controllers.…”

Section: Introductionmentioning

confidence: 99%

“…An extensive exposition of the use of SOS programming for controller design and domain of attraction analysis for continuous time systems is given in . Use of SOS programming for the design of polynomial controllers for polynomial continuous‐time systems is studied in and , while works on nonlinear discrete‐time systems include, for example, . In , the use of linear state feedback is studied, whereas addresses the synthesis of polynomial controllers, taking input saturation into account.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Vatani

Hovd

Olaru

2017

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

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.

show abstract

Section: Propositionmentioning

confidence: 99%

“…Substitute in the plant dynamics (7), the controller (4), and multiply with Q For point (2), evaluate the controller for Q x D Q x 1 v T T for any finite, constant vector v, and let Q…”

Section: Proofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Vatani

Hovd

Olaru

2017

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Based on this discussion, this work aims to develop robust stabilization conditions for discrete‐time constrained nonlinear systems with time‐varying parameters, considering the problems (i) and (ii) described previously. The class of systems considered in this research covers all systems that can be modeled by Difference‐Algebraic Representations (DAR), 26 also called in the literature as Recursive‐Algebraic Representations (RAR), 27,28 the discrete‐time counterpart of the Differential‐Algebraic Representations 29 . From a DAR, it is possible to obtain an exact representation of rational nonlinear systems in discrete‐time, as a set of algebraic and difference equations.…”

Section: Introductionmentioning

confidence: 99%

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Reis

Araujo

Tôrres

et al. 2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary This paper addresses the local stabilization problem of nonlinear systems described by Difference‐Algebraic Representations (DAR). A novel set of sufficient Linear Matrix Inequalities (LMI) conditions are developed to design gain‐scheduled state feedback controllers. The proposed approach uses parameter‐dependent Lyapunov functions and new auxiliary decision variables aiming to obtain less conservative results. Two optimization problems are proposed to either obtain the largest estimated Domain‐of‐Attraction (DOA) or minimize the ℓ2‐gain from the energy‐bounded disturbance input to the performance output. Furthermore, this investigation considers control input saturation and system states constrained in a polyhedral region. Numerical examples are provided to illustrate the effectiveness of the proposed methodology, showing favorable comparisons with recently published similar approaches.

show abstract

Regional Static Output Feedback Stabilization Based on Polynomial Lyapunov Functions for a Class of Nonlinear Systems

Reis,

Araújo,

Torres

et al. 2024

J Control Autom Electr Syst

View full text Add to dashboard Cite

Regional stabilization of rational discrete-time systems with magnitude control constraints

Cited by 4 publications

References 31 publications

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

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

Gain‐scheduled control design for discrete‐time nonlinear systems using difference‐algebraic representations

Regional Static Output Feedback Stabilization Based on Polynomial Lyapunov Functions for a Class of Nonlinear Systems

Contact Info

Product

Resources

About