Title :
Robust control of uncertain singular stochastic systems with markovian switching via proportional-derivative state feedback
Author :
Wang, Guibin ; Zhang, Qi
Author_Institution :
Sch. of Inf. & Control Eng., Liaoning Shihua Univ., Fushun, China
Abstract :
This study focuses on the problem of robust control for a class of uncertain singular stochastic Markovian jump systems via proportional-derivative state feedback controllers (PDSFCs). The uncertainties are not only in system matrices, such as state, input and derivative matrices, but also in mode transition rate matrix. New sufficient conditions for the existence of mode-dependent PDSFC are derived as linear matrix inequalities (LMIs) such that the closed-loop singular stochastic system is quadratically normal and quadratically stochastically stable (QNQSS). Especially, another PDSFC referred to be partially mode dependent is also given by a mode-dependent Lyapunov function. Numerical examples are used to show the effectiveness of the proposed methods.
Keywords :
Markov processes; PD control; closed loop systems; linear matrix inequalities; robust control; state feedback; stochastic systems; uncertain systems; LMI; Markovian switching; QNQSS; closed-loop singular stochastic system; derivative matrix; input matrix; linear matrix inequality; mode transition rate matrix; mode-dependent Lyapunov function; mode-dependent PDSFC; partially mode dependent; proportional-derivative state feedback controllers; quadratically normal; quadratically stochastically stable; robust control; state matrix; sufficient conditions; system matrices; uncertain singular stochastic Markovian jump systems; uncertainty;
Journal_Title :
Control Theory & Applications, IET
DOI :
10.1049/iet-cta.2011.0549