Preliminaries on Nonlinear Bounded Control for Time-Delay Systems (original) (raw)
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Stabilization of linear and nonlinear systems with time delay
Lecture Notes in Control and Information Sciences
This paper considers the problem of stabilizing linear and nonlinear continuous-time systems with state and measurement delay. For linear systems we address stabilization via fixed-order dynamic output feedback compensators and present sufficient conditions for stabilization involving a system of modified Riccati equations. For nonlinear systems we provide sufficient conditions for the design of static full-state feedback stabilizing controllers. The controllers obtained are delay-independent and hence apply to systems with infinite delay.
Improved Design of Nonlinear Control Systems with Time Delay
International Journal of Robotics and Control Systems
It is well known that time delay in nonlinear control systems may lead to the deterioration or even destabilization of the closed-loop systems. Therefore, specific analysis techniques and design methods are needed to be developed for nonlinear control systems in the presence of time delay. This chapter aims to give a broad overview of the stability and control of nonlinear time-delay systems. Firstly, we present some motivations and a comprehensive survey for the study of time-delay systems. Then, a brief overview of some control approaches is provided, specifically, the Lyapunov-Krasoviskii functional method for high-order polynomial uncertainties nonlinear time-delay systems, and nonlinear time-delay systems with nonlinear input, the Lyapunov-Razumikhin method for triangular structure nonlinear time-delay systems, dynamic gain control for full state time-delay systems. Finally, an application in chemical reactor systems is provided and some related open problems are discussed.
Nonlinear bounded control for time-delay systems
2001
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2005
This paper deals with a strong stability problem of a class of nonlinear time-varying control systems with state delays. Under appropriate growth conditions on the nonlinear perturbation, new sufficient conditions for the strong stabilizability are established based on the global null-controllability of the nominal linear system. These conditions are presented in terms of the solution of a standard Riccati differential equation. A constructive procedure for finding feedback stabilizing controls is also given.
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Advances in Difference Equations
This paper deals with the state and output feedback stabilization problems for a family of nonlinear time-delay systems satisfying some relaxed triangular-type condition. A new delay-dependent stabilization condition using a controller is formulated in terms of linear matrix inequalities (LMIs). Based on the Lyapunov-Krasovskii functionals, global asymptotical stability of the closed-loop systems is achieved. Finally, simulation results are shown to illustrate the feasibility of the proposed strategy.
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Journal of Dynamic Systems, Measurement, and Control, 2003
This paper gives a broad overview of the stability and control of time-delay systems. Emphasis is on the more recent progress and engineering applications. Examples of practical problems, mathematical descriptions, stability and performance analysis, and feedback control are discussed.
Exponential stability and stabilization of a class of uncertain linear time-delay systems
Journal of the Franklin Institute, 2009
This paper provide exponential stability conditions for a class of uncertain linear hybrid time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also timevarying. By using an improved Lyapunov-Krasovskii functional, a switching rule for the exponential stability is designed in terms of the solution of Riccati-type equations. The approach allows for computation of the bounds that characterize the exponential stability rate of the solution. An application to stabilization of linear control switching systems is given. Numerical examples are given to illustrate the results.
Comparative Study for Controller Design of Time-delay Systems
2009
Time delays are usually unavoidable in many mechanical and electrical systems. The presence of delay typically imposes strict limitations on achievable feedback performance in both continuous and discrete systems. The presence of the delay complicates the design process as it makes continuous systems to be infinite dimensional and it significantly increases the dimensions in discrete systems. Most of classical methods used controller design cannot be used with delayed systems. In this study, the delay will be modeled using different approaches such as Pad'e approximation and Smith Predictor in continuous system and modified z-transform in discreet systems. In this study, the delays are assumed to be constant and known. The delays in the system are lumped in the plant model. This study will show the design of stable and optimal controller for time-delay systems using algebraic Riccati equation solutions and PID control. This study will also present comparison between these controllers.
Exponential Convergence of Time-Delay Systems in the Presence of Bounded Disturbances
Journal of Optimization Theory and Applications, 2012
In this paper, the problem of control design for exponential convergence of state/input delay systems with bounded disturbances is considered. Based on the Lyapunov-Krasovskii method combining with the delay-decomposition technique, a new sufficient condition is proposed for the existence of a state feedback controller, which guarantees that all solutions of the closed-loop system converge exponentially (with a pre-specified convergence rate) within a ball whose radius is minimized. The obtained condition is given in terms of matrix inequalities with one parameter needing to be tuned, which can be solved by using a one-dimensional search method with Matlab's LMI Toolbox to minimize the radius of the ball. Two numerical examples are given to illustrate the superiority of the proposed method. Keywords Exponential convergence • Time-delay systems • Bounded disturbances 1 Introduction It is well-known that external disturbances are usually unavoidable to include in practical control systems due to modeling errors, linearization approximations, unknown Communicated by Martin Corless.