Delay-independent stabilization of linear systems with Antisymmetric Stepwise Configuration

Abstract

Wei has introduced the concept of antisymmetric step-wise configuration (ASC) of linear uncertain time varying systems and proved that it is necessary and sufficient for uncertain linear systems to have this configuration to be quadratically stabilizable by means of linear state variable feedback. However, because his condition is constructed on the basis of quadratic lyapunov punov function, his method is not applied if the system containes delays in the state variables. On the other hand, we have developed conditions for the delay independent stabilization of uncertain linear time-varying systems by means of memoryless linear state variable feedback. The obtained results have some similar forms to ASC and is equivalent in the most fundamental sence. To obtain this condition we have utilezed the convergence conditions of solutions of delay differential inequalities, which are free from the restriction of lyapunov functions. In this report the conditions so far obtained is developed and it is proved that generally to have ASC is also sufficient condtion for the delay independent stabilizability of linear uncertain delayed systems by means of linear state variable feedback, which is the same for Wei's method.