A New Approach to the H ∞ Design of Optimal Digital Linear Filters

Mathematical Problems in Engineering

2018

The tracking control of ∞ dynamic output feedback is proposed for the fuzzy networked systems of the same category, in which each system is discrete-time nonlinear and is missing measurable data. In other words, the loss of data packet occurs randomly in both the uplink and the downlink. The independent variables that are called the Bernoulli random variables are considered to design the loss of data packets. The method of parallel distributed compensation (PDC) in terms of the T-S fuzzy model is applied to investigate the dynamic controller of tracking control on the systems. Then, it is presented that the analytical ∞ performance of the output error between the reference model and the fuzzy model for the closed-loop system containing dynamic output feedback controller is proven. Furthermore, the achieved sufficient conditions in terms of LMIs ensure that the closed-loop system is stochastically stable in the ∞ sense. Finally, a numerical system is offered to show the effectiveness of the established technique.

Section: Introductionmentioning

confidence: 99%

H∞ Tracking Control of Fuzzy Dynamic Output for Nonlinear Networked System with Packet Dropouts

Mathematical Problems in Engineering

2018

“…Moreover, it is insensitive to the noise statistics and less sensitive than their H 2 counterparts to uncertainties [17][18][19]. Therefore, the H ∞ control scheme has attracted interest in the feedback control [20][21][22][23][24][25][26][27][28][29] since it was first introduced in 1989 [30]. Recently, the H ∞ control and filtering approaches were adopted in various settings and applications, such as [31][32][33] and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

Robust H ∞ sliding mode control with pole placement for a fluid power electrohydraulic actuator (EHA) system

Zhang

Liu

Int J Adv Manuf Technol

et al. 2014

In this paper, we exploit the sliding mode control problem for a fluid power electrohydraulic actuator (EHA) system. To characterize the nonlinearity of the friction, the EHA system is modeled as a linear system with a system uncertainty. Practically, it is assumed that the system is also subject to the load disturbance and the external noise. An integral sliding mode controller is proposed to design. The advanced techniques such as the H ∞ control and the regional pole placement are employed to derive the optimal feedback gain which can be calculated by solving a necessary and sufficient condition in the form of linear matrix inequality. A sliding mode control law is developed such that the sliding mode reaching law is satisfied. Simulation and comparison results show the effectiveness of the proposed design method.

“…In the classical filtering approach, the noise characteristics are assumed to be known, leading to the minimization of the norm of the transfer function from the process noise to the estimation error. The alternative filtering, which was first introduced in 1989 [2], has relaxed the boundedness assumption of the noise variance [12]. Over the past decades, much work has been done on the robust filtering problem in the presence of parameter uncertainties in various settings [3], [4], [18].…”

Section: Introductionmentioning

confidence: 99%

Robust $H_{\infty}$ Filtering for Time-Delay Systems With Probabilistic Sensor Faults

IEEE Signal Process. Lett.

Zhou

2009

Abstract-In this paper, a new robust filtering problem is investigated for a class of time-varying nonlinear system with norm-bounded parameter uncertainties, bounded state delay, sector-bounded nonlinearity and probabilistic sensor gain faults. The probabilistic sensor reductions are modeled by using a random variable that obeys a specific distribution in a known interval [ ], which accounts for the following two phenomenon: 1) signal stochastic attenuation in unreliable analog channel and 2) random sensor gain reduction in severe environment. The main task is to design a robust filter such that, for all possible uncertain measurements, system parameter uncertainties, nonlinearity as well as time-varying delays, the filtering error dynamics is asymptotically mean-square stable with a prescribed performance level. A sufficient condition for the existence of such a filter is presented in terms of the feasibility of a certain linear matrix inequality (LMI). A numerical example is introduced to illustrate the effectiveness and applicability of the proposed methodology.Index Terms-Linear matrix inequality (LMI), parameter uncertainties, robust filtering, sensor gain reduction.