Transmission delays lead to time lags, pulse phenomena caused by external environmental changes, logical behaviors, and inherent uncertainties are often inevitable. Therefore, the analysis and control of hybrid systems have not only significant scientific significance but also broad practical application value. However, the coupling and complexity of various variables make the analysis and control of hybrid systems exceptionally difficult. Members of this project team, based on modern control theory, impulse systems, stochastic analysis, and other theories, comprehensively use a series of analytical methods and matrix semi-tensor product tools to analyze and control hybrid systems. The research results not only enrich and develop the theory of hybrid systems but also provide new approaches and methods to solve actual control problems, with potential application prospects and strong frontier and innovative nature in the discipline. Key scientific findings are as follows: For this special class of hybrid systems with state mutation phenomena—pulse systems, the project team established or developed stability theory for pulse systems. By establishing new comparison theorems, it provided low-conservatism conditions for the stability of pulse systems; overcame the difficulties of the coexistence of time delay and pulse, obtained stability criteria for pulse-delay systems, and applied them to neural network systems; introduced for the first time the concept of finite-time stability for linear pulse systems and provided a concise criterion; further extended to singular systems and proposed design schemes for pulse suppression laws; based on a more general concept of finite-time stability, it provided stability criteria for finite-time stable linear time-varying singular systems and pulse suppression law design schemes, successfully utilizing the positive role of pulse control. 2. Hybrid systems where both pulses and Markov jumps exist have high nonlinearity, discontinuity, instantaneous variable mutation, The characteristics of random interference have brought difficulties to our research. The project team has used stability theory and comprehensive stochastic analysis methods to provide some criteria for the p-order moment stability of this system; by constructing nonlinear transformations, they established an equivalence relationship between the solutions of several classes of impulsive stochastic delay systems with pulse effects and their corresponding non-impulsive stochastic delay systems, breaking through the theoretical bottleneck of traditional methods such as applying Itô's formula, and obtained some important results on the stability of impulsive stochastic delay hybrid systems. 3. For Boolean networks with delays, the project team did not adopt the method of dimensionality expansion but instead utilized the relatively advanced international matrix semi-tensor product theory. Through providing iterative algorithms, they discovered the laws of interaction between logical systems and delays, and gave the necessary and sufficient conditions for controllability and observability. Avoided the 'curse of dimensionality'; Overcame research difficulties brought by uncertainty to logical systems, such as more complex topological structures and destruction of system attractors, etc., used matrix theory to give algebraic representation of the system, fully considered the inherent characteristics of probabilistic Boolean networks, and gave a low conservative controllability criterion for probabilistic Boolean networks. The project team published 4 monographs, published more than 200 papers in IEEE Transactions, Automatica, etc., and was included in SCIE, among which there were 14 papers in the top journals of information science and control science such as Automatica and IEEE Transactions on Automatic Control, and 7 authoritative IEEE transactions papers in the field of information science and control science. 7 papers were selected as highly cited papers by ESI. The total number of citations to our eight representative papers in SCIE is 643 (with 490 being self-citations), and the total number of citations in Google Scholar is 1070 (with 886 being self-citations). Our work has been cited by dozens of academicians and IEEE Fellows, including experts in cybernetics and mathematicians such as E. Valcher (president of the 2015 IEEE Control Systems Society), who have referred to our conclusions or used our methods to prove key lemmas. International peers not only directly use our conclusions or apply our methods to demonstrate major theorems but also evaluate them as 'original' and 'novel'. "Important issues," "Landmark," "Crucial theoretical results," etc. The American Mathematical Review: "The results are interesting." Four doctoral and four master's theses have been awarded as Shanghai Graduate Student Outstanding Dissertation Awards. Sun Jitao is currently an adjunct visiting professor at the University of Johannesburg and has always been an Elsevier Highly Cited Chinese Scholar.