Disturbance-Observer-Based Finite-Time Antidisturbance Control for Markov Switched Descriptor Systems With Multi-Disturbances and Intermittent Measurements
Kui Ding, Quanxin Zhu, Wei Xing Zheng
Abstract
This paper is concerned with the finite time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> composite anti-disturbance control problem for Markov switched descriptor systems with multiple disturbances and packet loss via a disturbance observer. Significantly, the switching topology of descriptor systems is controlled by nonhomogeneous Markov switching processes, whose time-varying transition probability is limited by a convex hull. Subsequently, a Bernoulli random variable is exploited to characterize the intermittent measurement mode behavior of controller-actuator packet loss. Furthermore, the stochastic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty} $ </tex-math></inline-formula> finite time boundiness of the composite system and simultaneously suppression and rejection of external disturbances are established by resorting to disturbance observer-based robust control (DOBC) strategy and a new stochastic Lyapunov function technique. More importantly, a relaxed variable method is provided to eliminate the coupling between Lyapunov variables and the system matrix in the process of stability analysis, instead of eliminating the coupling by means of commonly-used traditional inequalities, which effectively increases the flexibility of the obtained stable results and greatly reduces the computational complexity of controller/observer in the existing works. Finally, the effectiveness and practicability of the developed results are verified by two practical engineering models.