线性不确定时滞系统的时滞相关H^(∞)控制

DelayDependent H^(∞) Control for Linear Uncertain Systems with TimeDelay

基于动态耗散理论和微分对策理论,研究了确定性和不确定性线性时滞系统的时滞相关H∞状态反馈控制器的设计问题·将鲁棒控制器设计问题转化为非合作对策中目标函数求解鞍点问题,并针对确定性和不确定性线性时滞系统分别得到了控制器存在的充分条件·对于不确定线性时滞系统可以通过求解线性矩阵不等式进行时滞相关H∞鲁棒控制器设计,使系统内稳且具有H∞干扰衰减系数λ·而对于确定性线性时滞系统仅需要验证一个线性矩阵不等式,使设计问题得以简化·

?The design of H∞ state feedback controllers depending on the timedelays were considered for certain and uncertain linear systems with timedelay,based on dissipative dynamical system theory and differential game theory. The design of robust controllers was changed to the calculation of saddle point for a object function in noncooperative game. Two sufficient conditions were obtained respectively for certain and uncertain linear systems with timedelay respectively. The delaydependent H∞ robust controllers were designed for uncertain linear systems with timedelay by solving linear matrix inequalities. The controlled systems are internal stable and have the decrease coefficient λ of H∞ disturbance. For certain linear systems with timedelay, the design could be simplified by only checking a linear matrix inequalities.