Adaptive stabilizing state feedback controllers of uncertain dynamical systems with multiple time delays

Study of the Stabilization of Uncertain Nonlinear Systems Controlled by State Feedback

“…Note c P the matrix of change of base such that cc x = P x (5) which enables to describe the linearized system (1) without uncertainties in the controllable canonical form …”

“…A great number of works have been presented related to this problem [1][2][3][4][5][6]. For a nonlinear process in continuous time, whose evolution is described by a set of differential equations, the most commonly used model is represented in the state space.…”

Discrete-Time Adaptive Predictive Control with Asymptotic Output Tracking

“…For continuous-time systems with time delays, some of the useful tools in robust stability analysis have been well developed based on the Lyapunov's second method, the Lyapunov-Krasovskii theorem and the Lyapunov-Razumikhin theorem. Following its success in stability analysis, the utility of Lyapunov-Krasovskii functionals were subsequently explored in adaptive control designs for continuous-time time delayed systems Ge et al (2003;; Ge & Tee (2007);Wu (2000); Xia et al (2009);Zhang & Ge (2007). However, in the discrete-time case there dos not exist a counterpart of Lyapunov-Krasovskii functional.…”

Decentralized Adaptive Robust Stabilization for a Class of Uncertain Large Scale Interconnected Time-Delay Systems

“…By the continuity of the adaptive closed-loop large scale time-delay system described by (11) and (12), it is obvious that any solution (x, ƒÕ) (t; t0, x(t0), ƒÕ(to)) of the system is continuous.…”