Stability and stabilisability of switched discrete‐time systems based on structured Lyapunov functions

Lacerda, Márcio J.; Gomide, Thales da Silveira

doi:10.1049/iet-cta.2019.0485

Cited by 13 publications

(12 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Several research directions are suggested as the future works. The first one is related to use more efficient and less-conservative Lyapunov functions such as structured Lyapunov functions proposed in [49]. The second one is focus on the local or global optimization algorithms by developing more efficient numerical algorithms to achieve better performance indices such as convergence guarantee, higher convergence speed, and better solutions in the sense of the closeness to the real global optimum point.…”

Section: Resultsmentioning

confidence: 99%

“…The proof follows from the multiplication of Relations (49) and 51by h 1 , and Relations (50) and (52) by h 2 . Next, by…”

Section: T) Is the Solution Of The Same Optimization Problem Correspomentioning

confidence: 98%

“…The reason is that the former is in the category of the convex optimization problems for which efficient numerical algorithms handling the practical large-scale problems have been developed. In the convex programming, starting any initial point the convergence toward global optimum is always guaranteed and the sole concern is on the computational burden that in general is stated in terms of the number of unknown variables and number of LMI inequalities [49]. On the other hand, BMI based optimization problems are non-convex and exploring for a global optimum is an NP-hard problem.…”

Section: Examplesmentioning

confidence: 99%

See 2 more Smart Citations

On the global practical stabilization of discrete-time switched affine systems: application to switching power converters

Hejri

2020

Scientia Iranica

View full text Add to dashboard Cite

This paper presents new sufficient conditions as a set of Bilinear Matrix Inequalities (BMIs) for the global practical stabilization of discrete-time switched affine systems. The main contribution is on proposing the stability conditions based on a common quadratic Lyapunov function that can be used to stabilize the discrete-time switched affine systems around a desired equilibrium point for which it is not required to find any Schur stable convex combination of operating modes as a pre-processing stage, that needs special algorithms and is an NP-hard problem. The result is that the existing two-stage stabilization methods based on a pre-calculation of a Schur stable convex combination of operating modes are simplified to a single-stage method by which a high degree of applicability is obtained. The proposed stability conditions are developed in a way the size of the convergence ellipsoid is minimized. Moreover, it is not required the equilibrium point, around which the invariant set of attraction is constructed, be inside a predetermined set of attainable equilibrium points. The satisfactory operation of the proposed stability conditions is illustrated by an academic example and application on various DC-DC converters.

show abstract

Section: Resultsmentioning

confidence: 99%

“…The proof follows from the multiplication of Relations (49) and 51by h 1 , and Relations (50) and (52) by h 2 . Next, by…”

Section: T) Is the Solution Of The Same Optimization Problem Correspomentioning

confidence: 98%

Section: Examplesmentioning

confidence: 99%

See 1 more Smart Citation

On the global practical stabilization of discrete-time switched affine systems: application to switching power converters

Hejri

2020

Scientia Iranica

View full text Add to dashboard Cite

show abstract

“…A lei de chaveamento pode ser conhecida, e o chaveamento pode ser dependente do tempo ou dos estados, por exemplo. Porém, em outros casos a sequência de chaveamento pode não ser conhecida a priori e, com isto, resultados para a estabilidade e controle foram desenvolvidos considerando o chaveamento arbitrário (Daafouz et al, 2002;Lacerda and Gomide, 2020).…”

Section: Introdu ç ãOunclassified

“…Diferente do método apresentado Spagolla et al (2018), a técnica apresentada neste artigo não faz uso de busca escalar na solução das LMIs. A função de Lyapunov empregada neste artigo foi explorada para tratar sistemas incertos Pessim et al (2019) e sistemas chaveados Lacerda and Gomide (2020). Funções de Lyapunov estruturadas também foram consideradas em Lacerda and Seiler (2017).…”

Section: Introdu ç ãOunclassified

Controle de sistemas lineares positivos chaveados discretos no tempo: uma abordagem usando função de Lyapunov aumentada

Silva

Pessim

Lacerda

2021

Procedings Do XV Simpósio Brasileiro De Automação Inteligente

View full text Add to dashboard Cite

This paper presents new conditions in the form of Linear Matrix Inequalities capable of designing state-feedback controllers for discrete-time positive switched systems, subject to arbitrary switching. The presented conditions may be employed in the development of modedependent or mode-independent control strategies. Differently from existing conditions, the results are obtained through the use of an augmented Lyapunov function, that considers highorder shifted states in its state vector. Numerical experiments illustrate the performance and efficiency of the proposed approach in comparison with existing techniques from the literature. Resumo: Este artigo apresenta novas condições na forma de desigualdade matriciais lineares capazes de realizar o projeto de controladores por realimentação de estados para sistemas positivos chaveados de tempo discreto, sujeitos a chaveamento arbitrário. As condições apresentadas podem ser empregadas no desenvolvimento de estratégias de controle dependentes e independente dos modos. Diferentemente das condições existentes na literatura, os resultados foram obtidos com a utilização de uma função de Lyapunov aumentada, que considera taxas de deslocamento de ordem superior em seu vetor de estados. Exemplos numéricos ilustram o desempenho e a eficácia do método proposto em comparação com métodos existentes na literatura.

show abstract

Input‐to‐state stability for discrete‐time time‐varying impulsive switched delayed systems with asynchronous phenomena

Peng

2022

Asian Journal of Control

View full text Add to dashboard Cite

This paper studies the input-to-state stability (ISS) for a class of discrete-time time-varying impulsive switched delayed systems, in which the asynchronous phenomena are considered. Asynchronous phenomena here include two implications: asynchronous impulses and switches and asynchronous switching. The former means that the events, that is, impulses and switches, are not necessary to occur simultaneously, while the latter indicates that the actual switching modes and related controllers or specified modes do not coincide. Applying the mode-dependent concept to impulses and switches, both the improved Krasovskii-type and Razumikhin-type ISS criteria are provided. The time differences of Lyapunov functionals or functions here are sign-changing and time-varying, releasing from the traditional assumption that always requires negative definiteness. Meanwhile, in this paper, ISS or non-ISS subsystems and stabilizing or destabilizing impulses are taken into account. Finally, three numerical examples are given to illustrate the effectiveness of the proposed results.

show abstract

Stability and stabilisability of switched discrete‐time systems based on structured Lyapunov functions

Cited by 13 publications

References 34 publications

On the global practical stabilization of discrete-time switched affine systems: application to switching power converters

On the global practical stabilization of discrete-time switched affine systems: application to switching power converters

Controle de sistemas lineares positivos chaveados discretos no tempo: uma abordagem usando função de Lyapunov aumentada

Input‐to‐state stability for discrete‐time time‐varying impulsive switched delayed systems with asynchronous phenomena

Contact Info

Product

Resources

About