Liu X, Guo X, Liu W, Li Y. Finite-Time
H∞ Control for Time-Delay Markovian Jump Systems with Partially Unknown Transition Rate via General Controllers.
ENTROPY (BASEL, SWITZERLAND) 2023;
25:402. [PMID:
36981291 PMCID:
PMC10047916 DOI:
10.3390/e25030402]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Revised: 02/18/2023] [Accepted: 02/20/2023] [Indexed: 06/18/2023]
Abstract
This paper deals with the problems of finite-time boundedness (FTB) and H∞ FTB for time-delay Markovian jump systems with a partially unknown transition rate. First of all, sufficient conditions are provided, ensuring the FTB and H∞ FTB of systems given by linear matrix inequalities (LMIs). A new type of partially delay-dependent controller (PDDC) is designed so that the resulting closed-loop systems are finite-time bounded and satisfy a given H∞ disturbance attenuation level. The PDDC contains both non-time-delay and time-delay states, though not happening at the same time, which is related to the probability distribution of the Bernoulli variable. Furthermore, the PDDC is extended to two other cases; one does not contain the Bernoulli variable, and the other experiences a disordering phenomenon. Finally, three numerical examples are used to show the effectiveness of the proposed approaches.
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