An improved stability criterion for discrete-time time-delayed Lur’e systemwith sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur\u27e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach

SYNCHRONIZATION OF CHAOTIC SYSTEMS USING VARIABLE STRUCTURE CONTROLLERS

ABSTRACT In this paper a variable structure system based upon sliding mode control with time varying sliding surface and variable boundary layer is introduced to synchronize two different chaotic systems with uncertain parameters. The method is applied to Lur'e-Genesio chaotic systems, as drive-response systems to investigate the effectiveness and robustness of the controlling method. In addition the simulation is repeated with a conventional sliding mode to compare the performance of the proposed sliding mode technique with a simple sliding mode control. The results show the high quality and improved performance of the method presented in the paper for synchronization of different drive-response chaotic systems

Stability analysis of a phase plane control system

Many aerospace attitude control systems utilize a phase plane control scheme which includes nonlinear elements such as dead zone and ideal relay. Nonlinear control techniques such as pulse width modulation (PWM), describing functions, and absolute stability are implemented to determine stability. To evaluate phase plane control robustness, stability margin prediction methods must be developed. While PWM has been used to predict stability margins, in this research, describing functions and absolute stability are extended to predict stability margins. Time domain simulations demonstrate all techniques yield conservative gain margin results. A constrained optimization approach is also used to design flex filters for roll control. The design goal is to optimize vehicle tracking performance while maintaining adequate stability margins. Two filters are designed in this thesis; one meets PWM stability margin specifications and the other holds for Popov stability

Stability Analysis for Class of Switched Nonlinear Systems

Abstract-Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. The results are illustrated by numerical examples