scholarly journals Delay-DependentH∞Control for Descriptor Markovian Jump Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-16
Author(s):  
Jinghao Li ◽  
Qingling Zhang ◽  
Ding Zhai ◽  
Yi Zhang
Keyword(s):  
Convex Combination ◽  
Markovian Jump Systems ◽  
Delay Systems ◽  
Time Varying ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Bounded Real Lemma ◽  
Delay Dependent ◽  
Jump Systems ◽  
Varying Delay

This paper is concerned with the delay-dependentH∞control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribedH∞performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.

Disturbance-observer-based control for semi-Markovian jump systems with time-varying delay and generally uncertain transition rate

2020 ◽  
pp. 014233122096349
Author(s):  
Tianbo Xu ◽  
Xianwen Gao ◽  
Wenhai Qi
Keyword(s):  
Transition Rate ◽  
Disturbance Observer ◽  
Actuator Saturation ◽  
Markovian Jump Systems ◽  
Delay Systems ◽  
Time Varying ◽  
Markovian Jump ◽  
Time Varying Delay ◽  
Jump Systems ◽  
Varying Delay

The analysis result of disturbance-observer-based control (DOBC) for semi-Markovian jump systems (S-MJSs) with time-varying delay and generally uncertain transition rate (TR) is given in this paper. At present, there are still some urgent problems needed to be solved for S-MJSs such that conservative of stability, difficult of obtaining of TR in practical system, and the unexpected transient performance is always inevitable, such as larger overshoots and longer settling time. Unlike the existing methods, the proposed method considers the external disturbance, limitation on domain of control signal, uncertain parameters and time-varying delay in the S-MJSs. The piecewise analysis method for time-varying delay systems is extended to DOBC for S-MJSs. First of all, the sufficient condition of stochastic stability based on S-MJSs with more general TR is derived by piecewise Lyapunov-Krasovskii functional. Then, the disturbance observer is designed for estimating the actual disturbance, and the anti-disturbance controller is designed to deal with the control problem of S-MJSs. Furthermore, the problem of actuator saturation is addressed. Finally, two practical example is employed to testify the correctness of the proposed methods.

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