A Dynamic Event-Triggered Approach to H∞ Control for Discrete-Time Singularly Perturbed Systems With Time-Delays and Sensor Saturations

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 51; no. 11; pp. 6614 - 6625
• Main Authors: Ma, Lei, Wang, Zidong, Cai, Chenxiao, Alsaadi, Fuad E.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H ∞ control; Algorithms; Computational geometry; Control systems; Control systems design; Controllers; Convexity; Discrete time systems; Discrete-time singularly perturbed systems (DTSPSs); dynamic event-triggered mechanism (DETM); Feedback control; H-infinity control; Mathematical programming; Network reliability; Numerical stability; Output feedback; Packet transmission; Performance indices; Perturbation methods; Protocols; sensor saturations; Singular perturbation; Stability analysis; Symmetric matrices; time-delays; Upper bounds
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2019.2958529

In this article, the <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> control problem is investigated for a class of discrete-time singularly perturbed systems (DTSPSs) with time-delays and sensor saturations. In order to save the network bandwidth with satisfactory communication reliability during the signal transmissions, a dynamic event-triggered mechanism (DETM) is put forward to regulate the data-packet transmissions from the saturated sensors to the proposed controller. By constructing a novel Lyapunov-Krasovskii functional dependent on the singular perturbation parameter (SPP), the dynamics of the DTSPSs under the DETM are rigorously analyzed, and an output-feedback controller design scheme is then developed to ensure that, for any SPP not exceeding a prescribed upper bound, the closed-loop system is asymptotically stable with a guaranteed <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> performance index. By resorting to the convex programming techniques, the desired controller gain is parameterized in light of the feasible solutions to a set of matrix inequalities. Finally, the effectiveness and merits of the proposed algorithm are demonstrated by a simulation example.