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Finite time stabilization of the four tanks system: extensions to the uncertain systems. (English) Zbl 1406.93236

Summary: We consider the finite time stability and stabilization of linear systems described in continuous time. First, we provide a condition for the stability over time using the state transition matrix standard. Then we give conditions to design a state feedback control that stabilizes the system over time. In some cases where there is uncertainty in the system model, the previous conditions are extended to a certain class of uncertain systems. The considered uncertainties are the polytopic and norm bounded ones. To reveal the proposed approach, an application to the four tanks system was made.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C41 Control/observation systems with incomplete information
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
93B52 Feedback control
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References:

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