Abstract
This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials.
Highlights
Time-delay systems are systems in which a time lag occurs between the input of the system and its consequent output; such systems may be electronic, mechanical, biological, manufacturing process, or chemical systems, among many others
The use of mathematical representations of physical systems to mathematically describe interactions among system components allows us to analyze critical stability properties that ensure good performance of the dynamic system as well as to prevent its physical destruction. The use of these mathematical models introduces some errors into the stability analysis because mathematical representations of physical processes do not always characterize dynamic behavior successfully
This problem has been addressed by including dynamic uncertainty [3] or parametric uncertainty [4,5] in the mathematical model; in that manner, we refer to robust stability when uncertainty is considered in the mathematical model
Summary
Time-delay systems are systems in which a time lag occurs between the input of the system and its consequent output; such systems may be electronic, mechanical, biological, manufacturing process, or chemical systems, among many others. This work presents a robust stabilization approach based on the frequency domain for interval plants with parametric uncertainty and uncertain time-delay This result is based on the verification of selected polynomial properties using Kharitonov’s polynomials in a way that allows us to establish sufficient conditions to guarantee robust stability. This condition is essential for determining the controller that stabilizes the interval plant with a time delay by applying conditions similar to those established in the loop-shaping technique and by parameterizing controllers using stable polynomials constructed from classical orthogonal polynomials.
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