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Stability analysis and $H_{∞}$ control of discrete T-S fuzzy hyperbolic systems

100%
Duan R., Li J., Zhang Y., Yang Y., Chen G.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 1
133-145
EN
This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T-S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T-S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and $H_{∞}$ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T-S fuzzy hyperbolic model with the discrete T-S fuzzy linear one are also given to illustrate the advantage of our approach.
2
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Robust stability of positive continuous-time linear systems with delays

88%
Busłowicz M.
International Journal of Applied Mathematics and Computer Science
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2010
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tom 20
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nr 4
665-670
EN
The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.
3
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Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties

88%
Rauh A., Minisini J., Hofer E.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
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nr 3
425-439
EN
Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.
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