Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities

Abstract

This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems(MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional(LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities(LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less.

Faults Modeling in Networked Environment and Its Tolerant Control with Multiple Simultaneous Faults

“…It is, therefore, very important to consider partly known TPs in the Markov chain. This is why stability criteria are proposed for Markovian jump systems (MJSs) with partially known TPs in [6,7], and results with less conservative outcomes are presented in [8][9][10]. The conditions for the stability and stabilization of NCSs with partially known TPs are presented in [11].…”

Lower Triangular Factor-Based Fault Estimation and Fault-Tolerant Control for Descriptor Markovian Jump Systems with Multiple Faults

“…Descriptor systems theory is an essential branch of modern control theory [1,6]. Meanwhile, Markovian jump systems (MJSs) are a special kind of multimodal stochastic hybrid system, and the modes can switch from one to another at different times [7,8]. Descriptor Markovian jump systems (DMJSs) can be modeled when descriptor systems experience sudden changes such as environmental mutation, component failures, and changes in subsystem interconnection.…”

Reguladores robustos recursivos para sistemas lineares sujeitos a saltos Markovianos com atraso no estado

“…Particularmente, Dzung e Hien (2017) propuseram um controlador de realimentação de estado dependente do modo para SLSMA nominal. Uma condição de estabilização estocástica de sistemas Markovianos nominais com atraso variante no tempo e dois processos de Markov homogêneos mutuamente não correlacionados é fornecido por Li et al (2021). Para SLSMA com incertezas limitadas em norma, Qiu et al (2015) fornece uma lei de controle de realimentação de estado atrasado dependente de duas cadeias de Markov mutuamente independentes.…”

“…Exemplo 6.2. Considere o SLSMA incerto de tempo discreto, conforme descrito em (6.1)-(6.2) com três modos de operação, sendo as matrizes paramétricas nominais estudadas em (LI et al, 2021):…”

“…Exemplo 7.1. Considere um SLSMAP de tempo discreto conforme descrito em (7.1) com três modos de operação, sendo as matrizes paramétricas propostas em (LI et al, 2021) , sendo 𝜙 0 (𝑘) = 𝑥 0 , ∀𝑘 ≤ 0. Além disso, considera-se a matriz de probabilidade de transição incerta ̂︀ P 𝛿 modelada limitada em norma em (QIU et al, 2015), a qual pode ser representada por um politopo de 2vértices obtidos quando Δ 𝜃 𝑘 ,𝑘 = −1 e Δ 𝜃 𝑘 ,𝑘 = 1, dadas por O desempenho do RRR-MTIP (Algoritmo 7.1) é analisado por meio de uma comparação com a abordagem dada em termos de LMIs desenvolvida por Qiu et al (2015, Teo.…”