Abstract
The problem of stochastic finite‐time guaranteed cost control is investigated for Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time‐varying norm‐bounded disturbance. Firstly, the definitions of stochastic singular finite‐time stability, stochastic singular finite‐time boundedness, and stochastic singular finite‐time guaranteed cost control are presented. Then, sufficient conditions on stochastic singular finite‐time guaranteed cost control are obtained for the family of stochastic singular systems. Designed algorithms for the state feedback controller are provided to guarantee that the underlying stochastic singular system is stochastic singular finite‐time guaranteed cost control in terms of restricted linear matrix equalities with a fixed parameter. Finally, numerical examples are given to show the validity of the proposed scheme.
Highlights
Singular systems are referred to as descriptor systems or generalized state-space systems and describe a larger family of dynamic systems
We investigate finitetime guaranteed cost control of one class of continuous-time stochastic singular systems
The novelty of our study is that stochastic finite-time stability, stochastic finite-time bounded and stochastic finite-time guaranteed cost control are investigated for one family of Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time-varying norm-bounded disturbance
Summary
Singular systems are referred to as descriptor systems or generalized state-space systems and describe a larger family of dynamic systems. Some appealing results were obtained to guarantee finite-time stability, finite-time boundedness, and finite-time stabilization of different systems including linear systems, nonlinear systems, and stochastic systems; for instance, see the papers in 29–35 and the references therein. The novelty of our study is that stochastic finite-time stability, stochastic finite-time bounded and stochastic finite-time guaranteed cost control are investigated for one family of Markovian jumping singular systems with uncertain transition probabilities, parametric uncertainties, and time-varying norm-bounded disturbance. Λmin P and λmax P denote the smallest and the largest eigenvalue of matrix P , respectively Matrices, if their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations
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