CAJ | 학술논문

周期间歇控制是一类特殊形式的切换控制，周期间歇控制下的动态系统可视为由一个受控子系统和一个自由子系统组成的周期切换系统。针对周期间歇控制系统动态特征，提出运用时变切换Lyapunov函数方法研究一类非线性系统的周期间歇镇定问题。在控制器激活区间和控制器关闭区间，分别引入不同的时变Lyapunov函数来分析系统的稳定性。利用凸组合技术，将系统稳定性条件表示为一组线性矩阵不等式，通过求解该组线性矩阵不等式，容易获得使系统稳定的控制窗口宽度上界。在稳定性分析的基础上，基于一组线性矩阵不等式的可行解，给出了控制增益矩阵的参数化表示。与现有的时不变Lyapunov函数方法相比，所提出的时变切换Lyapunov函数方法能有效地利用系统的动态特性，降低结果的保守性。数值例子验证了文中方法的有效性和优越性。
주기간헐공제시일류특수형식적절환공제，주기간헐공제하적동태계통가시위유일개수공자계통화일개자유자계통조성적주기절환계통。침대주기간헐공제계통동태특정，제출운용시변절환Lyapunov함수방법연구일류비선성계통적주기간헐진정문제。재공제기격활구간화공제기관폐구간，분별인입불동적시변Lyapunov함수래분석계통적은정성。이용철조합기술，장계통은정성조건표시위일조선성구진불등식，통과구해해조선성구진불등식，용역획득사계통은정적공제창구관도상계。재은정성분석적기출상，기우일조선성구진불등식적가행해，급출료공제증익구진적삼수화표시。여현유적시불변Lyapunov함수방법상비，소제출적시변절환Lyapunov함수방법능유효지이용계통적동태특성，강저결과적보수성。수치례자험증료문중방법적유효성화우월성。
Periodic intermittent control is a special form of switching control.The dynamical system under periodic intermittent control can be viewed as a periodic switched system consisting of a con-trolled subsystem and a free subsystem.In view of the dynamic characteristics of the periodic inter-mittent control systems, a time-varying switching Lyapunov function based method is proposed to solve periodic intermittent stabilization problem for a class of nonlinear systems.In the intervals that the controller is active and in the intervals that the controller is closed, different time-varying Lya-punov functions are introduced to analyze the stability of the system under consideration.By using convex combination technique, the derived stability condition is formulated into linear matrix ine-qualities so that the upper bound of the width of the control window can be easily obtained by solving the set of linear matrix inequalities.Based on the obtained stability results, a parameterized repre-sentation of the intermittent control gain matrix is presented in terms of the feasible solution of a set of linear matrix inequalities.Compared with the existing time-invariant Lyapunov function based methods, the proposed time-varying switched Lyapunov function method can effectively utilize the dynamic characteristics of the considered system, and thus reduce the conservatives of the achieved results.A numerical example is presented to show the validity and superiority of the proposed method.