This paper deals with the stabilization of TakagiSugeno fuzzy models. Using non-quadratic Lyapunov function, new sufficient stabilization criteria with PDC controller are established in terms of Linear Matrix Inequality. Finally, a stabilization condition for uncertain system is given.

This work builds off of recent work on rapidly exponentially stabilizing control Lyapunov functions (RES-CLF) and presents a novel method to address actuator saturation in bipedal walking. The proposed method employs quadratic programming (QP) to implement CLF-based controllers, enabling directly incorporating user-specified input bounds into the controller. We show that even with increasingly ...

Lyapunov drift is a powerful tool for optimizing stochastic queueing networks subject to stability. However, the most convenient drift conditions often provide results in terms of a time average expectation, rather than a pure time average. This paper provides an extended drift-plus-penalty result that ensures stability with desired time averages with probability 1. The analysis uses the law of...

this paper proposes a hybrid control scheme for the synchronization of two chaotic duffing oscillator system, subject to uncertainties and external disturbances. the novelty of this scheme is that the linear quadratic regulation (lqr) control, sliding mode (sm) control and gaussian radial basis function neural network (grbfnn) control are combined to chaos synchronization with respect to extern...

This paper deals with the problem of tracking control for Takagi-Sugeno fuzzy model. An LMI (Linear Matrix Inequality) formulation is suggested to make possible the convergence of the state vector of the continuous-time system to a desired one using a new approach, called MultiQuadratic Fuzzy Lyapunov (MQFL). A fourth order unstable nonlinear system is studied to illustrate the efficiency of th...

Exponential stability of hybrid systems using a Lyapunov approach is considered in this paper. The continuous part of the hybrid system is described by nonlinear differential equations that depend on a discrete state. The discrete state changes when certain switch sets are reached. By using piecewise quadratic forms of the Lyapunov function candidates, it is shown how the stability conditions c...

In this paper Kharitonov's theorem for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. I t is shown that if the four Hermite matrices corresponding to the four Kharitonov extreme polynomials are positive definite, the Hermit...