Global Practical Tracking by Output Feedback for Nonlinear Systems with Unknown Growth Rate and Time Delay

Abstract

This paper is the further investigation of work of Yan and Liu, 2011, and considers the global practical tracking problem by output feedback for a class of uncertain nonlinear systems with not only unmeasured states dependent growth but also time-varying time delay. Compared with the closely related works, the remarkableness of the paper is that the time-varying time delay and unmeasurable states are permitted in the system nonlinear growth. Motivated by the related tracking results and flexibly using the ideas and techniques of universal control and dead zone, an adaptive output-feedback tracking controller is explicitly designed with the help of a new Lyapunov-Krasovskii functional, to make the tracking error prescribed arbitrarily small after a finite time while keeping all the closed-loop signals bounded. A numerical example demonstrates the effectiveness of the results.

Survey of duality between linear quadratic regulation and linear estimation problems for discrete-time systems

“…Over the past few decades, the study of time delays has exerted great interest of plenty of scholars [10][11][12][13][14]. According to different kinds of time delay, many results have sprung up, such as communication delay [15,16], control input delay [17][18][19][20], state-dependent delay [21][22][23][24], state-independent delay [25,26], output delay [27,28], distributed delay [29][30][31][32], time-varying delay [33,34]. For example, communication links are usually imperfect and the limited bandwidth may result in delays.…”

Practical output tracking for a class of uncertain nonlinear time-delay systems via state feedback

“…Compared with study the stabilization problem contain time-delay, the theory of output tracking control developed slower. In the case when the nonlinearities contain timedelay, for the output tracking problems, some interesting results have been obtained [14][15][16]. However, in [14 -16] only considered special case for the system (1), i.e., 1  i p case.…”

“…Since the prove of the claim (17) is very similar [4][5]14], so omitted here. Using the inductive argument above, we can conclude that at the -th step, there exists a state feedback controller of the form…”

Adaptive Parallel Simultaneous Stabilization of a Class of Nonlinear Descriptor Systems via Dissipative Matrix Method

“…In this paper, motivated by the Hamiltonian function method [2,[19][20][21][22][23][24][25][26][27][28][29], we apply the structural properties of dissipative matrices to investigate the adaptive parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems for a class of NDSs via output feedback law [30,31], and propose a new approach, called the dissipative matrix method, to study NDSs. Firstly, under an output feedback law, two NDSs are transformed into two nonlinear differential-algebraic systems by nonsingular transformations, and a sufficient condition of impulse-free is given for two closed-loop systems.…”