Robust analysis and superstabilization of chaotic systems

Abstract

Superstable behavior is a practically important feature of dynamic systems. In the work we study the peculiarities of superstability achievement as applied to chaotic systems. We show a class of chaotic systems, for which a technique of finding optimal superstabilizing regulators can be presented. The efficiency of superstability conditions for the robust analysis and stabilization in the presence of parametric instability is demonstrated in the work.

Superstabilization of Descriptor Continuous-Time Linear Systems via State-Feedback Using Drazin Inverse Matrix Method

“…Local and global stability criteria for a population model with two age classes were considered in [27]. A special class of stable systems are superstable systems with more restricted dynamics requirements, i.e., with the norm of the state vector decreasing monotonically to zero [28][29][30].…”

State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

“…The value of the free response of an asymptotically stable system decreases to zero over time, but it may considerably increase in the initial part of the trajectory. In superstable systems, which are a subclass of asymptotically stable systems, state variables are limited by the value of the norm of the state vector, which decreases monotonically to zero over time [28][29][30].…”

“…Such systems provide some practically important properties, e.g., superstability (as opposed to stability) remains under the presence of time-varying and nonlinear perturbations, which allows researchers to solve problems relating to the synthesis of robust systems easily. Moreover, superstable systems ensure the elimination of peaks or sharp increases in the state vector trajectory [28][29][30].…”

Superstabilization of positive linear electrical circuit by state-feedbacks

“…From Gershgorin theorem and (6) it follows that the state variables u i (t), i = 1, …, n of positive electrical circuits have not overshoots. See also [17][18][19]. □…”

“…Stability of continuous-time and discrete-time linear systems with inverse state matrices has been analyzed in [15] and positive stable minimal realization of fractional linear systems in [16]. Superstability and superstabilization of dynamical systems have been considered in [17][18][19].…”