For the control synthesis problem,an LMI-based condition was derived to build a state feedback controller ensuring the closed-loop system is asymptotically stable and has an L 2-gain smaller than a positive scalar gamma.

Then,based on Lyapunov function and the backstepping design technique,a state feedback controller for the slow subsystem is also constructed,which enables the closed-loop system to be internally stable for all bounded interference and satisfies the arbitrarily small bounded L2 gain from exogeneous interfe.

It is shown that L2 gain performance and the control law can be obtained by solving a set of Linear Matrix Inequalities that is numerically feasible with commercially available software.

The sufficient condition that such a system can keep up its robustly asymptotic stability if the L2 gain is given is put forward,which is described by linear matrix inequality.

Secondly,some notions and conceptions are given for the L2-gain problem of time-delay Hamiltonian systems.

In order to reduce conservative performances resulted in by the application of the Lyapunov function to the analysis of a linear parameter-varying system,the relationships of the stability and L2-gain of the system with the subsection and changing rate of parameters were investigated.

A scheme for an adaptive neural network L2-gain controller was proposed for nonlinear systems with uncertainty.

For an affine nonlinear system affected by internal and external disturbances, the discontinuous state feedback controllers are built by using switching technique and multiple Lyapunov function method with switching laws designed to ensure that for all allowable uncertainties the relevant closed-loop system possesses the prescribed L_2-gain and is asymptotically stable.

First,the Lyapunov function and controller for each sub-system are designed by means of Backstepping methods,and then,they are integrated to form the entire Lyapunov function and controller,which not only satisfies the requirement of stability,but also satisfies some performance indices of the L_2-gain.

Spacecraft robust attitude control design based on L_2-gain stabilization;

Novel nonlinear L2 gain control method for doubly-fed induction motor based on port controlled Hamiltonian model

The paper proposes a novel nonlinear L2 gain control method based on the averaged port controlled Hamiltonian(PCH) model of active power filter(APF).

This paper proposes a novel adaptive L2 gain control algorithm with sliding dissipative damping and limitation for Active power filter (APF) based on its averaged port controlled hamitonian (PCH) model.