## 1 Introduction  
Markov jump systems are composed of a series of continuous time or discrete time subsystems, and the jump between the modes is determined by the Markov chain. Many practical stochastic mutation systems can be modeled using Markov jump systems. Thus, the jump systems have been extensively studied and many useful results have been obtained. The stochastic stability of a Markov jump system was proposed by [PERSON] and [PERSON] [1]. Many researchers have discussed the problems surrounding stochastic stability and stochastic admissibility for Markov jump systems, such as stability for discrete-time systems [2; 3; 4]. For continuous-time systems, [PERSON] solved stability and stabilization problems [5]; the stability of singular hybrid systems was discussed in [6] and a nonlinear Markov system was discussed in [7; 8; 9]. On the other hand, a model reference adaptive control (MRAC) constructs a reference model to characterize the desired control performance of a closed-loop system [10], which has been widely used in the industry and theoretical control. The authors of [11] designed a tracking controller for the switched systems based on a reference model. There are some applications used in different fields of MRAC, such as economics [12], vehicles [13; 14], sleep monitoring [15], polysolenoid linear motors [16], and the visual servo system [17]. In [18], the model reference control problem for the Markov system was first discussed. However, the model reference controls for Markov jump systems with circular or elliptical orbits, such as satellites, did not appear until 2017 (in [19]). However, he does not take the incompleteness of the state and unknown transition rates (TRs) into consideration. In practical engineering, the state of the system is difficult to obtain. Thus, the observer that obtains the system state by the output is also widely used in the control field for a traditional system, e.g., the traditional Luenbergerobserver [20; 21; 22; 23] or the robust observer [24; 25]. In [26], a novel robust observer was designed, moreover, some sliding observers were reviewed in [27; 28]. For Markov systems, observers were designed, such as a proportional integral observer [29], whose performance is excellent but does not fit high-order systems. [PERSON] studied the state estimation and sliding mode control of the Markov jump system [30] and the mode-dependent observer [31] for the discrete Markov system. [PERSON] designed an observer for Markov jump systems [32], which can directly obtain the state estimation without any supplementary design. In this paper, the state was obtained by a series of transformations. Many studies are based on the condition that the transition matrix is completely known. In engineering, some values of transition matrices are hard to obtain, while some are completely inaccessible. Thus, the unknown part of the transition matrix comes into view, e.g., the information is incomplete in Markov chains or games [33; 34; 35], and the TRs are partially unknown [36; 37; 38; 39; 40]. In [38], the author assumed that the lower bound of the unknown self-transition rate was known and successfully solved the stability problem. However, in practical applications, the above conditions are difficult to meet. In 2014, [PERSON] attempted to solve the problem of a completely unknown situation of the self-transition rate in [41], but the proof process was wrong. In [42], [PERSON] proposed sufficient and necessary conditions for the resolution with partly unknown transition rates. However, the author just set up a new function that was still a sufficient condition. 2021, In [43], the author solved the H\(\infty\) filtering of a discrete Markov jump system with unknown transition rates, where the self-transition rate could be absolutely unknown. However, the self-transition rate of a discrete jump system is positive, while the self-transition rate of a continuous jump system is negative, so the above method does not apply to the continuous system.