Factors such as time delays caused by transmission delays, impulse phenomena caused by changes in the external environment, logical behavior and inherent uncertainties are often inevitable. Therefore, the analysis and control of hybrid systems not only have important scientific significance but also have extensive practical application value. However, the coupling and mixing of various variables can make the analysis and control of hybrid systems extremely difficult. Based on modern control theory, impulse systems, stochastic analysis and other theories, the project team members comprehensively use a series of analysis methods and matrix semi-tensor product tools to analyze and control the hybrid system. The research results not only enrich and develop hybrid system theory, but also provide new ways and methods to solve practical control problems. They have potential application prospects and are highly cutting-edge and innovative in the subject. The key scientific discoveries are as follows: 1. For this special type of hybrid system with state mutation phenomenon-impulsive systems, the project team established or developed a stability theory for impulsive systems. By establishing a new comparison theorem, a low conservative condition for the stability of impulsive systems is given. The stability criterion for impulsive systems with time-delay is obtained and applied to neural network systems by overcoming the difficulty of both time delay and impulse. The concept of finite time stability of linear impulsive systems is introduced for the first time and concise criterion is given. It is further extended to singular systems and a design scheme for the impulsive ballast law is given. Based on the more general concept of finite-time stability, the finite-time stability criterion and impulse ballast law design scheme for linear time-varying singular systems are provided, and the positive role of impulse control is successfully utilized. 2. The hybrid system with both pulses and Markov jumps has the characteristics of high nonlinearity, discontinuity, instantaneous sudden changes in variables, random interference, etc., which brings difficulties to our research. The project team used stability theory to synthesize random analysis methods to give some criteria for the stability of the p-order moment of the system; By constructing nonlinear transformations, the equivalent relations between the solutions of several classes of stochastic differential delay systems with impulsive actions and their corresponding stochastic differential delay systems without impulsive actions are established, which breaks through& the theoretical bottleneck of using traditional methods such as Itocirc; formula, and obtains some important results on the stability of stochastic delay hybrid systems with impulsive actions. 3. For Boolean networks with time delays, the project team did not adopt the method of expanding dimensions. Instead, it used the internationally advanced semi-tensor product theory of matrices to discover the laws of the interaction between the logical system and time delays by giving an iterative algorithm, and gave sufficient and necessary conditions for its controllability and observability, avoiding the disaster of dimension; overcoming the research difficulties brought by uncertainty to the logical system, such as the more complex topology structure, destroying the system's attractors, etc., using matrix theory to give the algebraic representation of the system, and fully considering the inherent characteristics of probability Boolean networks, a low-conservative controllability criterion for probability Boolean networks is given. The project team published 4 monographs, which were published in IEEE Trans., Automatica and others published more than 200 papers and were included in SCIE, including Automatica, the top journals in the fields of information science and control science, and IEEE

There are 14 papers on Trans. Automatic Control and 7 papers on authoritative IEEE Transactions in the fields of information science and control science. 7 papers were selected as ESI highly cited papers. The total number of citations for the eight representative works SCIE is 643(he cited 490 times), and the total number of citations for Google Scholar is 1070(he cited 886 times). Dozens of academicians and IEEE Fellow, such as E. Cybernetics experts and mathematicians such as Valcher (president of 2015 IEEE control system society) cited our work. International colleagues not only directly use our conclusions or use our methods to prove the main lemma, but also evaluate them as ldquo;original rdquo;, ldquo; novel rdquo;important

issues rdquo;, ldquo;landmark rdquo;, ldquo; critical theoretical results rdquo; etc. American Mathematical Review: ldquo;results are interesting rdquo;. 4 doctoral and 4 master's thesis are excellent degree thesis for postgraduate students in Shanghai City. Sun Jitao is currently a distinguished visiting professor at the University of Johannesburg and has been a highly cited scholar in Elsevier China.