تجزیه و تحلیل ساختاری پایداری سیستم کنترل

Stability of control systems is one of the central subjects in control theory. The classical asymptotic stability theorem states that the norm of the residual between the state trajectory and the equilibrium is zero in the limit. Unfortunately, it does not in general allow computing a rate of convergence, whereas proving exponential stability is notoriously complicated. This work proposes to revisit the asymptotic stability theory with the aim of computing convergence rates using constructive analysis which is a mathematical tool that realizes equivalence between certain theorems and computational algorithms. The overall goal of the current study matches with the trend for introducing formal verification tools into control theory. Besides existing approaches, constructive analysis, suggested within this work, can also be considered for formal verification of control systems. A computational example is provided that demonstrates extraction of a convergence certificate for a dynamical system.