Robust H∞ Finite-Time Control for Discrete Markovian Jump Systems with Disturbances of Probabilistic Distributions

Abstract

This paper is concerned with the robust H ∞ finite-time control for discrete delayed nonlinear systems with Markovian jumps and external disturbances. It is usually assumed that the disturbance affects the system states and outputs with the same influence degree of 100%, which is not evident enough to reflect the situation where the disturbance affects these two parts by different influence degrees. To tackle this problem, a probabilistic distribution denoted by binomial sequences is introduced to describe the external disturbance. Throughout the paper, the definitions of the finite-time boundedness (FTB) and the H ∞ FTB are firstly given respectively. To extend the results further, a model which combines a linear dynamic system and a static nonlinear operator is referred to describe the system under discussion. Then by virtue of state feedback control method, some new sufficient criteria are derived which guarantee the FTB and H ∞ FTB performances for the considered system. Finally, an example is provided to demonstrate the effectiveness of the developed control laws.

Finite‐horizon fault estimation under imperfect measurements and stochastic communication protocol: Dealing with finite‐time boundedness

“…Let > 0, 0 ≤ e 1 ≤ , e 2 ≥ 0,N ∈N 0 , and p (0) > 0 be known. The estimation error dynamics (19) is finite-time bounded and the fault estimation errorz (k) achieves the H ∞ performance index (22) with (e 1 , e 2 , , p (0), N) if there exist sequences of matrices { p (k) > 0} 1≤k≤N,p∈{1,2, … ,n } , {Π 1 (k) ≥ 0} 1≤k≤N , and {Π 2 (k) ≥ 0} 1≤k≤N such that inequality (24) and the following condition are simultaneously satisfied:…”

“…Let > 0, 0 ≤ e 1 ≤ , e 2 ≥ 0,N ∈N 0 , and p (0) > 0 be known. The estimation error dynamics (19) is finite-time bounded and the fault estimation errorz (k) meets the H ∞ performance index (22) with (e 1 , e 2 , ,…”

“…In the context of practical fault estimation, it is always desirable to develop estimators that meet several different performance constraints such as the H ∞ performance index describing the insensitivity against external disturbances and the finite‐time boundedness (FTB) characterizing the capability of restraining the state variables below a known upper bound over a finite‐time interval. It is noted that, in the past decade, the research on the FTB performance has gained much attention and a large mount of related research topics have been found in the existing literature (see, eg, other works). For instance, a feedback controller has been constructed in the work of Chen et al to ensure the FTB of the closed‐loop system with a given disturbance‐attenuation rate.…”

“…It is noted that, in the past decade, the research on the FTB performance has gained much attention and a large mount of related research topics have been found in the existing literature (see, eg, other works). For instance, a feedback controller has been constructed in the work of Chen et al to ensure the FTB of the closed‐loop system with a given disturbance‐attenuation rate. In the work of Mathiyalagan et al, the FTB and finite‐time dissipativity have been analyzed for delayed networked cascade control systems and the obtained results have been successfully applied on a power plant boiler‐turbine system.…”

Nonlinear Predictive Control of a Hydropower System Model

“…In [22], multi-zone buildings were identified by an artificial neural network and controlled by predictive control techniques. The robust H  finite-time control method for a discrete system was discussed in [23]. Compared with the abovementioned methods, nonlinear predictive control theory is easier to apply in practice, and can be combined with traditional methods, which takes advantages of both traditional methods and predictive control as shown later in this paper.…”