This Lyapunov functional is shown to be the solution to a functional Hamilton-Jacobi-Bellman (HJB) equation. Sufficient conditions for optimality are then provided in the form of a steady-state ...

The main focus is on differential and algebraic Riccati equations appearing in control and model order reduction, as well as algebraic Lyapunov equations for, e.g., balanced truncation. The underlying ...

The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple ...

Equation (4) describes the linear dependence of the mean firing ... We then apply the analysis of the largest Lyapunov exponent to characterize the dynamics of this I&F system. We mathematically ...

An equation is a statement with an equals sign, stating that two expressions are equal in value, for example \(3x + 5 = 11\) Solving an equation means finding the value or values for which the two ...

Autonomous Underwater Vehicle are widely used in industries, such as marine resource exploitation and fish farming, but they are often subject to a large amount of interference which cause poor ...