In this paper we define strong and weak common quadratic Lyapunov functions (CQLF’s) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the non-existence of a strong CQLF, for a pair of LTI systems, is characterised by easily verifiable algebraic conditions. These conditions are found to play an important role in provin...

In this paper, a new approach for the stability analysis of continuous-time Takagi–Sugeno (T-S) fuzzy system is proposed. The universe set is divided to subregions, and piecewise quadratic Lyapunov function is then found for each of them. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov functio...

We consider nonlinear systems dx=dt = f(x(t)) where Df(x(t)) is known to lie in the convex hull of L matrices A1, : : : , AL 2 R n . For such systems, quadratic Lyapunov functions can be determined using convex programming techniques [1]. This paper describes an algorithm that either nds a quadratic Lyapunov function or terminates with a proof that no quadratic Lyapunov function exists. The alg...

In this paper we derive a necessary and sufficient condition for the existence of a common diagonal quadratic Lyapunov function for a pair of positive linear time-invariant (LTI) systems.

in this paper, a new method is derived for the existence of a common quadratic Lyapunov function for Robust Stability Analysis of Fuzzy Elman Neural Network using joint spectral radius spectral radius of Matrix.

The recently developed technique for computation of piecewise quadratic Lyapunov functions is specialized to Lyapunov functions that are piecewise linear. This establishes a unified framework for computation of quadratic, piecewise quadratic, piecewise linear and polytopic Lyapunov functions. The search for a piecewise linear Lyapunov function is formulated as a linear programming problem, and ...

We address the safety-critical control problem for systems whose dynamics evolve on manifolds using the concepts of control Lyapunov functions (CLFs) and control Barrier functions (CBFs). We first extend the concepts of CLFs and CBFs from Cartesian spaces to manifolds, resulting in geometric CLFs and CBFs. We then formulate a state-dependent online quadratic program (QP) that imposes the constr...

We consider the basic model of virus dynamics with noncytolytic loss of infected cells for the infection with viral hepatitis B. Stability of the infection-free steady state and existence, uniqueness and stability of the infected steady state is investigated. The stability results are given in terms of the basic reproductive number R0. Here, we perform the global stability analysis using two te...

This paper addresses the problem of model-based global stability analysis of discrete-time Takagi–Sugeno multiregional dynamic output controllers with static antiwindup filters. The presented analyses are reduced to the problem of a feasibility study of the Linear Matrix Inequalities (LMIs), derived based on Lyapunov stability theory. Two sets of LMIs are considered candidate derived from the c...