This paper proposes a novel approach based on Lyapunov function method to analyse the stability of photovoltaic (PV) systems. The Lyapunov function is formulated using the method of quadratic forms, i.e., Krasovskii’s method. The stability of the photovoltaic systems under different operating conditions is analysed based on the formulated Lyapunov function. A comparison of stability analysis us...

We present sufficient and necessary conditions for exponential stability of autonomous nonlinear dynamical systems using piecewise quadratic Lyapunov functions. The necessary conditions are given as a converse theorem guaranteeing the existence of a global piecewise quadratic Lyapunov function for an exponentially stable system.

In this paper piecewise quadratic stability of closed-loop affine Takagi-Sugeno (ATS) fuzzy systems with linear state-space submodels in the consequent of rules is addressed. The control law is assumed in the form of Parallel Distributed Compensation (PDC). Stability analysis of the closed-loop system is based on piecewise quadratic Lyapunov functions. This technique reduces conservatism of cla...

Abstract The problem of estimating the Domain of Attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities (LMIs) is proposed. Moreover, for the...

The problem of estimating the domain of attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities (LMIs) is proposed. Moreover, for the case of ...

This paper presents a new approach for the stability analysis of TakagiSugeno (T-S) fuzzy systems. An idea is investigated to use piecewise quadratic Lyapunov function with low amount of computations. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov function, we derive stability conditions that...

In this paper the existence of a quadratic control Lyapunov function for bilinear systems is considered. The existence of a control Lyapunov function ensures the existence of a control law which ensures the global asymptotic stability of the closed loop control system. In this paper we will derive conditions for the existence of a control Lyapunov function for bilinear systems. These conditions...

The paper deals with the stability properties of linear discrete-time switched systems with polytopic sets of modes. The most classical and viable way of studying the uniform asymptotic stability of such a system is to check for the existence of a quadratic Lyapunov function. It is known from the literature that letting the Lyapunov function depend on the time-varying switching parameter improv...

It is shown that for smooth nonlinear systems conditions for the existence of a Lyapunov function that guarantees uniform exponential stability can be formulated as linear inequalities deened pointwise in the state-space when assuming a general linearly parameterized class of smooth non-quadratic Lyapunov-function candidates. Hence, computation of the Lyapunov function involves the solution of ...

This article deals with the design of quadratic and linear dynamic output feedback controllers for systems to ensure, on one hand, local exponential stability origin in closed-loop form and, other increase an estimate basin attraction as large possible. The introduction a term controller allows us consider same class dynamics studied system. Here, our approach is Lyapunov function respect exten...