In this paper, we investigate the structure of several convex cones that arise in the study of Lyapunov functions. In particular, we consider cones associated with quadratic Lyapunov functions for both linear and non-linear systems, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, we present som...

In this paper, the structure of several convex cones that arise in the study of Lyapunov functions is investigated. In particular, the cones associated with quadratic Lyapunov functions for both linear and non-linear systems are considered, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, some t...

This paper studies the global asymptotic stability of a class of fuzzy systems. It demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant (LTI) switching systems. A necessary condition and a sufficient condition for the stability of such systems are given, and it is shown that under the sufficient condition, a common Lyapunov function exists for the LTI ...

This paper addresses closed-loop stability analysis of PID controlled local model networks. The proposed method allows to investigate exponential or asymptotic stability of the closed-loop system. For this purpose a common quadratic Lyapunov function is used as stability criterion. Due to the fact that the Lyapunov approach requires a state-space model a suitable closed-loop state-space system ...

The paper deals with the stability properties of linear discrete-time switched systems with polytopic sets of modes. The most classical 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 improves the chan...

The paper addresses the problem of stabilizing discrete-time systems subject to time varying polytopic uncertainty. Non stationary quadratic Lyapunov functions are derived for synthesis in a Poly-Quadratic Lyapunov function concept which avoids in a large extent the conservatism linked with the classical single Lyapunov function quadratic approach. The state space feedback synthesis problem is ...

In recent years, there has been significant interest in the study of stability analysis and con‐ troller synthesis for Takagi-Sugeno(T-S) fuzzy systems, which has been used to approximate certain complex nonlinear systems [1]. Hence it is important to study their stability analysis and controller synthesis. A rich body of literature has appeared on the stability analysis and synthesis problems ...

In this paper we obtain a homogeneous, continuous, quadratic and strict Lyapunov function for Levant’s Second Order Differentiator. Since its derivative is a non quadratic, discontinuous, homogeneous form its negative definiteness is determined using some new inequalities, providing coarser bounds than Young’s inequalities.

SIRS models with delay times (discrete or distributed) are studied. By means of Lyapunov functionals, we establish the global stability conditions of the equilibrium states. We will make ingenious linear combination of common quadratic, composite quadratic and Volterra-type functionals, for obtain a suitable Lyapunov functionals.

This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods tha...