We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapuno...

In this paper we consider the stabilization of hybrid systems with both continuous and discrete dynamics via predictive control. To deal with the presence of discrete dynamics we adopt a “hybrid” control Lyapunov function approach, which consists of using two different functions. A Lyapunov-like function is designed to ensure finite-time convergence of the discrete state to a target value, whil...

Many UPS inverters used in todays technology are more efficient and reliable. In this paper we propose a UPS inverter controlled by space vector PWM technique with extended Lyapunov function control strategy which is formed by the energy storage in inductor and capacitor making the system to converge at an equilibrium point when the energy is continuously dissipated. Therefore, an extended Lyap...

The paper gives new results that contribute to the development of a stability theory for 2D nonlinear discrete and differential systems described by a state-space model of the Roesser form using an extension of Lyapunov’s method. One of the main difficulties in using such an approach is that the full derivative or its discrete counterpart along the trajectories cannot be obtained without explic...

The aim of this work is to present an entropy-like Lyapunov function based dynamic feedback design technique for quasi-polynomial and Lotka-Volterra systems. It is shown, that the dynamic feedback design problem is equivalent to the feasibility of a bilinear matrix inequality. The problem is also formulated as a control Lyapunov function based feedback design when the Lyapunov function paramete...

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We...

In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bou...