scholarly journals Linear Matrix Inequalities for an Iterative Solution of Robust Output Feedback Control of Systems with Bounded and Stochastic Uncertainty

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3285
Author(s):  
Andreas Rauh ◽  
Swantje Romig
Keyword(s):  
Linear Matrix Inequalities ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Iterative Solution ◽  
Simultaneous Optimization ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Optimization Task ◽  
State Observers

Linear matrix inequalities (LMIs) have gained much importance in recent years for the design of robust controllers for linear dynamic systems, for the design of state observers, as well as for the optimization of both. Typical performance criteria that are considered in these cases are either H2 or H∞ measures. In addition to bounded parameter uncertainty, included in the LMI-based design by means of polytopic uncertainty representations, the recent work of the authors showed that state observers can be optimized with the help of LMIs so that their error dynamics become insensitive against stochastic noise. However, the joint optimization of the parameters of the output feedback controllers of a proportional-differentiating type with a simultaneous optimization of linear output filters for smoothening measurements and for their numeric differentiation has not yet been considered. This is challenging due to the fact that the joint consideration of both types of uncertainties, as well as the combined control and filter optimization lead to a problem that is constrained by nonlinear matrix inequalities. In the current paper, a novel iterative LMI-based procedure is presented for the solution of this optimization task. Finally, an illustrating example is presented to compare the new parameterization scheme for the output feedback controller—which was jointly optimized with a linear derivative estimator—with a heuristically tuned D-type control law of previous work that was implemented with the help of an optimized full-order state observer.

scholarly journals Quantized Dissipative Observer-Based Output Feedback Control for a Class of Markovian Descriptor Jump Systems with Communication Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Muhammad Shamrooz Aslam ◽  
Xisheng Dai
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequalities ◽  
Output Feedback ◽  
Nonlinear Dynamical Systems ◽  
Output Feedback Control ◽  
Descriptor Systems ◽  
Space Representation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Jump Systems

This paper investigates the problem of quantized dissipative observer-based output feedback control of Markovian descriptor jump systems with unavailable states, appearing networked-induced delay. The descriptor systems are presented as Markovian jump systems which give a more realistic presentation for a variety of nonlinear dynamical systems than conventional state-space representation. To accomplish the objective, a uniform framework is employed to design the delayed Markov observer-based controller and event-triggered scheme. Additionally, we provided the ℋ∞ and ℒ2-ℒ∞ and dissipative performance indices which are robust against the disturbances with time-varying delays. Moreover, a novel Lyapunov–Krasovskii functional is considered to guarantee the closed loop for stochastic stability analysis of the Markovian descriptor jump system. The solvability of Lyapunov–Krasovskii functional results in the formation of linear matrix inequalities. The controller and observer gains can be obtained by solving the linear matrix inequalities. Simulations are performed to validate the proposed scheme.

Vibration control of base-isolated structures using mixed H2/H∞ output-feedback control

2009 ◽  
Vol 223 (6) ◽  
pp. 809-820 ◽  
Author(s):  
H R Karimi ◽  
M Zapateiro ◽  
N Luo
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Design Methodology ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
Building Structures ◽  
Matrix Inequalities ◽  
Closed Loop System

A mixed H2/ H∞ output-feedback control design methodology for vibration reduction of base-isolated building structures modelled in the form of second-order linear systems is presented. Sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities. A controller that guarantees asymptotic stability and a mixed H2/ H∞ performance for the closed-loop system of the structure is developed, based on a Lyapunov function. The performance of the controller is evaluated by means of simulations in MATLAB/Simulink.

scholarly journals Multivariable Static Output Feedback Control of a Binary Distillation Column using Linear Matrix Inequalities and Genetic Algorithm

2017 ◽  
Author(s):  
Kalpana R. ◽  
Harikumar Kandath ◽  
Senthilkumar J. ◽  
Balasubramanian G. ◽  
Abhay S. Gour
Keyword(s):  
Genetic Algorithm ◽  
Linear Matrix Inequalities ◽  
Simulation Study ◽  
Output Feedback ◽  
Distillation Column ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Static Output

The current work addresses the control of two-input two-output (TITO) Wood and Berry model of a binary distillation column. The controller design problem is formulated in terms of multivariable H∞ control synthesis. The controller structure takes the form of simplest static output feedback (SOF) control. The controller synthesis is performed using a hybrid approach of blending linear matrix inequalities (LMI) and genetic algorithm (GA). The performance of the static output feedback controller is compared with three other controllers designed for Wood and Berry model available in the literature. The first simulation study is performed for the case of tracking a unit step command in the presence of a step change in output disturbance. A second simulation study is performed for rejecting a change in sinusoidal output disturbance.

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