Exponential <i>H</i>_∞ Output Control for Switching Fuzzy Systems via Event-Triggered Mechanism and Logarithmic Quantization

This paper investigates the problem of exponential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> output control for switching fuzzy systems, considering both impulse and non-impulse scenarios. Unlike previous research, where the average dwell time (ADT: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>τ</mi><mi>a</mi></msub></semantics></math></inline-formula>) and the upper bound of inter-event intervals (IEIs: <i>T</i>) satisfy the condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mi>a</mi></msub><mo>≥</mo><mfrac><mrow><mo form="prefix">ln</mo><mi>μ</mi><mo>+</mo><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo><mi>T</mi></mrow><mi>α</mi></mfrac><mo>=</mo><mfrac><mrow><mo form="prefix">ln</mo><mi>μ</mi><mo>+</mo><mi>β</mi><mi>T</mi></mrow><mi>α</mi></mfrac><mo>+</mo><mi>T</mi></mrow></semantics></math></inline-formula>, implying that frequent switching is difficult to achieve, this paper demonstrates that by adopting the mode-dependent event-triggered mechanism (ETM) and a switching law, frequent switching is indeed achieved. Moreover, the question of deriving the normal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>2</mn></msub></semantics></math></inline-formula> norm constraint is solved through the ADT method, although only a weighted <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>2</mn></msub></semantics></math></inline-formula> norm constraint was obtained previously. Additionally, by constructing a controller-mode-dependent Lyapunov function and adopting logarithmic quantizers, the sufficient criteria of exponential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>H</mi><mo>∞</mo></msub></semantics></math></inline-formula> output control problem are presented. The validity of established results is demonstrated by a given numerical simulation.