This paper presents an original practical criterion of global stability analysis of nonlinear polynomial systems. This criterion derived from the application of the Lyapunov direct method with a quadratic function generalizes the famous Lyapunov stability condition for linear systems. Useful mathematical transformations have allowed the formulation of the obtained conditions as an LMI (Linear M...

We study the stability of an equilibrium arbitrarily switched, autonomous, continuous-time systems through computation a common Lyapunov function (CLF). The switching occurs between finite number individual subsystems, each which is assumed to be linear. present linear programming (LP) based approach compute continuous and piecewise affine (CPA) CLF compare this with different methods in litera...

This paper addresses the stabilisation of discrete-time switching linear systems (DTSSs) with control inputs under arbitrary switching, based on the existence of a common quadratic Lyapunov function (CQLF). The authors have begun a line of work dealing with control design based on the Lie-algebraic solvability property. The present paper expands on earlier work by deriving sufficient conditions...

We consider the stability of the feedback connection of a linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program. By generalizing the class of candidate Lyapunov functions we improve on existing results in the literature. A Lyapunov function is constructed via the S-procedure from quadratic constraints established using the Karush-Kuhn-Tuc...

We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function which is the ratio of two polynomials (i.e., a rational function). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sums of squares certificates and hence such a Lyapunov fun...

We present a novel development of randomized algorithms for quadratic stability analysis of sampled-data systems with memoryless quantizers. The specific randomized algorithm employed generates a quadratic Lyapunov function and leads to realistic bounds on the performance of such systems. A key feature of this method is that the characteristics of quantizers are exploited to make the algorithm ...

We present efficiently verifiable sufficient conditions for the validity of specific NP-hard semi-infinite systems of semidefinite and conic quadratic constraints arising in the framework of Robust Convex Programming and demonstrate that these conditions are “tight” up to an absolute constant factor. We discuss applications in Control on the construction of a quadratic Lyapunov function for lin...

Quadratic stability has enabled, mainly via the linear matrix inequality framework, the analysis and design of a nonlinear control system from the local matrices of the system’s Takagi–Sugeno (T–S) fuzzy model. It is well known, however, that there exist stable differential inclusions, hence T–S fuzzy models whose stability is unprovable by a globally quadratic Lyapunov function. At present, li...

In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar neutral type time delay equation is considered. The construction of the functionals depends on the so-called Lyapunov functions which satisfy a delay equation with additional boundary conditions. It is shown that these functionals admit lower and upper quadratic bounds. Exponential estimates...