Absolute and Relative Stability. A control system is called absolutely stable if the controlled transfer function Hd(s) from the reference signal yd(s) to the output signal y(s) has all of its poles in the open left half plane. One technique for determining absolute stability of a control system is the Routh-Hurwitz stability analysis technique. This very useful technique is presented in Sectio...

This study analyzes the absolute stability in P and PD type fuzzy logic control systems with both certain and uncertain linear plants. Stability analysis includes the reference input, actuator gain and interval plant parameters. For certain linear plants, the stability (i.e. the stable equilibriums of error) in P and PD types is analyzed with the Popov or linearization methods under various ref...

The lambda-omega class of reaction-diffusion equations has received considerable attention because they are more amenable to mathematical investigation than other oscillatory reaction-diffusion systems and include the normal form of any reaction-diffusion system with scalar diffusion close to a standard supercritical Hopf bifurcation. Despite this, detailed studies of the dynamics predicted by ...

The present paper establishes results for the robust absolute stability of a class of nonlinear continuous-time systems with time-varying matrix uncertainties of polyhedral type and multiple time-varying sector nonlinearities. By using the variational method and the Lyapunov Second Method, criteria for robust absolute stability are obtained in di1erent forms for the given class of systems. Spec...

This paper presents a new result on absolute exponential stability (AEST) of a class of continuous-time recurrent neural networks with locally Lipschitz continuous and monotone nondecreasing activation functions. The additively diagonally stable connection weight matrices are proven to be able to guarantee AEST of the neural networks. The AEST result extends and improves the existing absolute s...

The problem of absolute stability of a feedback loop of an abstract diierential system in Hilbert spaces is considered. Applications of Popov's type frequency domain criteria and of the Kalman-Yakubovich Lemma for the construction of Lyapunov functions are illustrated, in two situations pertaining distributed sytems. Finally, a new criterion for absolute stability of a class of parabolic system...

A 3-degrees-of-freedom (DOF) bilateral haptic system can be modeled as an 2-port network where each port connects to a termination defined by 3 inputs and 3 outputs. The stability analysis of such systems is not trivial due to dynamic coupling across the different DOFs of the robots, the human operators, and the physical/virtual environments, and unknown dynamics of the human operators and the ...

Trilateral haptic systems can be modeled as threeport networks. Analysis of coupled stability of a three-port network can be accomplished in either the passivity or the absolute stability frameworks assuming all three ports are connected to passive but otherwise unknown terminations. This paper first introduces our recent results in terms of extending Raisbecks passivity criterion and Llewellyn...

In this paper, the problem of delay-dependent robust absolute stability of uncertain multiple time-delayed Lur'e systems with sector-bounded nonlinearity is investigated. The nonlinearity is assumed to be both time-invariant and time-varying. Based on the Lyapunov-Krasovskii stability theory and matrix decomposition method, some delay-dependent sufficient conditions for the robust absolute stab...

The problems of absolute stability and existence of forced oscillations for systems with sector restricted nonlinearities are considered. An overview of the results for systems described by ordinary differential equations with constant and periodic coefficients is presented. A result is obtained on exponential absolute stability for systems described by ordinary differential equations. Next, a ...