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摘 要：将耗散理论的二次型供给率中的矩阵Q推广到正定的情况。进而研究了在状态转移概率未知的情况下一类连续时间非线性广义马尔可夫跳变系统的严格耗散控制问题。在应用范围更广的Willems耗散性定义的基础上，首先基于一类Lyapunov函数，给出了相应的随机容许的条件，然后设计导数比例反馈控制器，通过一系列的矩阵构造和合同变换，将双线性矩阵不等式（BMI）转化为可用LMI工具箱解决的线性矩阵不等式（LMI）。最后通过数值算例并结合Matlab给出实例，证明其可行性。
关键词：非线性广义马尔可夫跳变系统;转移概率部分未知;耗散控制;P-D反馈
Abstract：The matrix Q in the quadratic supply rate of dissipative theory is extended to the case of positive definite. Furthermore， the strictly dissipative control problem for a class of continuous time nonlinear singular Markov jump systems with unknown state transition rates is studied. Based on the more widely used definition of Willems dissipativity， firstly， based on a class of Lyapunov functions， the stochastically admissible conditions are given， and then the proportional derivative feedback controller is designed. Through a series of matrix construction and contract transformation， bilinear matrix inequality （BMI） is transformed into linear matrix inequality （LMI） which can be solved by LMI toolbox. Finally， a numerical example is given to prove its feasibility.
Key words：nonlinear singular Markov jump systems; partly unknown transition rates; strict dissipativity; P-D state feedback
近年來，马尔可夫系统由于可以更好的描述复杂系统而受到广泛关注[1]。耗散系统理论在广义系统中也有诸多的应用[2]，由于耗散性存在的一般性引起学者关注。一些学者考虑了广义马尔可夫系统具有耗散性质的稳定性问题[3-5]，文献[6][7]基于Q
关键词：非线性广义马尔可夫跳变系统;转移概率部分未知;耗散控制;P-D反馈
Abstract：The matrix Q in the quadratic supply rate of dissipative theory is extended to the case of positive definite. Furthermore， the strictly dissipative control problem for a class of continuous time nonlinear singular Markov jump systems with unknown state transition rates is studied. Based on the more widely used definition of Willems dissipativity， firstly， based on a class of Lyapunov functions， the stochastically admissible conditions are given， and then the proportional derivative feedback controller is designed. Through a series of matrix construction and contract transformation， bilinear matrix inequality （BMI） is transformed into linear matrix inequality （LMI） which can be solved by LMI toolbox. Finally， a numerical example is given to prove its feasibility.
Key words：nonlinear singular Markov jump systems; partly unknown transition rates; strict dissipativity; P-D state feedback
近年來，马尔可夫系统由于可以更好的描述复杂系统而受到广泛关注[1]。耗散系统理论在广义系统中也有诸多的应用[2]，由于耗散性存在的一般性引起学者关注。一些学者考虑了广义马尔可夫系统具有耗散性质的稳定性问题[3-5]，文献[6][7]基于Q