Up till now, many investigations about stability of multiform switched systems have been carried out see, for instance, and references therein. Its motivation comes from the fact that many practical systems are inherently multimodal and the fact that some of intelligent control methods are based on the idea of switching between different controllers. Recently, switched system becomes a research hotspot.
![proof of bibo stability condition proof of bibo stability condition](https://slideplayer.com/slide/17694312/105/images/11/BIBO+Stability+Example.jpg)
For instance, in, BIBO stability criterion is derived for a three-dimensional fuzzy two-term control system, in, the problem on BIBO stabilization for a system with nonlinear perturbations is studied by discussing the existence of the positive definite solution to an auxiliary algebraic Riccati matrix equation, in, based on linear matrix inequality techniques, the stabilization criterion for uncertain time-delay system is presented to guarantee that bounded input can lead to bounded output, and in, BIBO stability for feedback control systems with time delay is studied through investigating the boundedness of the solutions for a class of nonlinear Volterra integral equations. Consequently, bounded-input bounded-output (BIBO) stability analysis of dynamical systems has attracted many scholars’ attention.
#Proof of bibo stability condition free#
As an important system performance index, BIBO stability means that any bounded input yields a bounded output and can be considered in many aspects, such as the free system dynamics, the basic single or double loop modulators, and the issues connected with bilinear input/output maps. Since the existence of time delays may lead to oscillation, divergence, or instability, considerable effort has been devoted to this area.
![proof of bibo stability condition proof of bibo stability condition](https://images.slideplayer.com/16/5215648/slides/slide_2.jpg)
Time delay is a source of instability and poor performance and appears in many dynamic systems, for example, biological systems, chemical systems, metallurgical processing systems, nuclear reactor systems, and electrical networks.
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The numerical simulation is carried out to demonstrate the effectiveness of the results obtained in the paper. Based on the Lyapunov-Krasovskii functional theory, new BIBO stabilization criteria are established in terms of delay-dependent linear matrix inequalities. The problem of bounded-input bounded-output (BIBO) stability is investigated for a class of delay switched systems with mixed time-varying discrete and constant neutral delays and nonlinear perturbation.