Practical Stability of Impulsive Control Systems

Impulsive Control Systems

Impulsive control systems arose from classical control systems described by differential equations where the control functions could be unbounded. Passing to the limit of trajectories whose velocities are changing very rapidly leads to the state vector to “jump”, or exhibit impulsive behavior. The mathematical model in this thesis uses a differential inclusion and a measure-driven control, and ...

On stability of perturbed impulsive differential systems

The notion of Lipschitz stability of impulsive systems of differential equations (DEs) was introduced. In this paper, we will extend the notion of eventual stability to impulsive systems of DEs and extend the notion of Lipschitz stability of impulsive systems of DEs to a new type of stability called eventual Lipschitz stability. Some criteria and results are given. Our technique depends on Liap...

Robust Stability of Singularly Impulsive Dynamical Systems

In this paper, we present results of the robust stability analysis for the class of nonlinear uncertain singularly impulsive dynamical systems. We present sufficient conditions for the robust stability of a class of nonlinear uncertain singularly impulsive dynamical systems. The problem of evaluating performance bounds for a nonlinear-nonquadratic hybrid cost functional depending upon a class o...

A Note on Practical Stability of Nonlinear Vibration Systems with Impulsive Effects

Exponential Practical Stability of Nonlinear Impulsive Systems: Converse Theorem and Applications

This paper investigates the practical exponential stability of equilibrium for impulsive systems. Stability theorem and converse stability theorem are established by employing the second Lyapunov method. These theorems are used to analyze the practical exponential stability of the zero solution of perturbed impulsive systems and cascaded impulsive systems.