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 of nonlinear uncertain singularly impulsive dynamical systems is considered. It turns out that the cost bound can be evaluated in closed form as long as the hybrid cost functional is related in a specific way to an underlying Lyapunov function that guarantees robust stability over a prescribed uncertainty set. Then, results for the case of uncertain singularly impulsive dynamical systems are presented. The results obtained for the nonlinear case are further specialized to linear singularly impulsive dynamical systems

Generalized State-Dependent Scaling for Local Optimality, Global Inverse Optimality, and Global Robust Stability 12

This paper provides a solution to an inverse optimal robust control problem for uncertain nonlinear systems. A new version of robust backstepping is proposed in which inverse optimality is achieved through the selection of generalized state-dependent scaling factors. Like other robust backstepping methods, this design is always successful for uncertain nonlinear systems in strict-feedback form. The class of cost functionals allowed in the inverse optimal design is such that the uncertainty structure and desired level of global robustness can be prescribed a priori. Furthermore, the inverse optimal control law can always be designed such that its linearization is identical to a linear optimal control law for the linearized system with respect to a prescribed quadratic cost functional