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The problem of $ L_1 $ L 1 output tracking control of positive linear systems in finite time is addressed in this paper. By constructing a linear copositive Lyapunov–Krasovskii functional, some sufficient conditions are achieved to ensure that the states are finite-time bounded and the measurement outputs have $ L_1- $ L 1 − gain performance for given systems, respectively. Next, a state feedback controller is designed to ensure that the output signals of the tracking system can effectively trace the specified signals of reference model with finite-time boundedness and $ L_1 $ L 1 -gain performance. Finally, an example is given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This article focuses on state and output tracking control for positive continuous-time linear systems without overshoot. Linear state feedback controllers are designed respectively to ensure both the system state, and output can unilateral track the reference state and output. In addition, using Lyapunov direct method, the exponential convergence rate of tracking system is calculated. A numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of positive L1$$ {L}_1 $$ filter for positive Markovian jump systems (PMJSs) with adaptive event‐triggered mechanism and quantization. Considering the mode jump of the system, a new adaptive event‐triggered condition is established, which not only can regulate the communication threshold according to the error of dynamic systems, but also can avoid the asynchronous phenomenon between the system mode and the filter mode. In order to further reduce the burden of communication, a new positive L1$$ {L}_1 $$ filter with the quantized measure system output is developed, and the design condition which ensures the filter error system to be stochastically stable with L1$$ {L}_1 $$ performance is presented which can be solved in terms of linear programming (LP) technique. It is illustrated that there is no Zeno phenomenon. The proposed results are applied to the power allocation in a mobile telecommunication system, and it is shown that compared with the existing results, the event‐triggered filter of this paper has some advantages. [ABSTRACT FROM AUTHOR]

This article investigates the nonfragile guaranteed cost (GC) control problem of discrete-time impulsive switched Takagi–Sugeno (T–S) fuzzy systems with input quantization and asynchronous switching. The model-dependent dynamic quantizers are applied to obtain the quantized input signal. To deeply study the GC performance analysis and GC control problems in the presence of quantization, asynchronous switching, and impulses, a novel piecewise cost function containing the quantized input instead of normal input is applied in this article. By using the mode-dependent average dwell time approach and introducing a class of Lyapunov-like functions allowing to increase during the asynchronous period, new sufficient conditions are established to guarantee the asymptotical stability with the GC performance index for the impulsive switched T–S fuzzy systems with quantized control input and asynchronous switching. Then, new design conditions about the nonfragile GC controllers and dynamic quantizers of impulsive switched T–S fuzzy systems are obtained in the form of linear matrix inequalities. Finally, a numerical example and a practical example are provided. [ABSTRACT FROM AUTHOR]

The quantized guaranteed cost static output feedback control problem is investigated for a class of discrete-time nonlinear networked control systems in this article. In this article, the Takagi–Sugeno fuzzy model is put to use for the representation of considered nonlinear networked control systems, where local nonlinear models instead of local linear models are used in the Takagi–Sugeno fuzzy model. Two different dynamic quantizers are applied to quantize the control input and measurement output, respectively. Different from some previous work, a novel guaranteed cost performance function including the quantized control input is used in this article. Through using the $S$ -procedure and introducing some auxiliary scalars, sufficient conditions for the design of guaranteed cost static output feedback controller and dynamic quantizers are obtained in the form of linear matrix inequalities. Finally, the applicability of the proposed method is illustrated through the application in nonlinear mass-spring-damper mechanical system. [ABSTRACT FROM AUTHOR]

Summary: In this work, the problem of adaptive state regulation is addressed via output feedback for a wide class of large‐scale systems with strongly interconnected time‐delay nonlinearities. A design approach of partially decentralized adaptive controller is proposed, which gives a novel pair of reduced‐order observer and controller with nonidentifier‐based double adaptive gains. Compared with the existing results, the growth restrictions imposed on the interconnections are relaxed, where the growth rate includes not only an unknown constant but also the nonpolynomial functions of system output. The double dynamic gains are capable of compensating both the uncertain nonpolynomial growth rate and the unknown time‐varying delay. By constructing novel Lyapunov–Krasovskii functionals and combining dynamic‐scaling technique with Barbălat's lemma, it is shown that global adaptive state asymptotical regulation is achieved, that is all the closed‐loop signals are bounded, and the states of system and observer tend to zero as time goes to infinity. Finally, a simulation example is given to illustrate the proposed control scheme is independent of time delay and well universal. [ABSTRACT FROM AUTHOR]

This article investigates stochastic stability of positive singular Markovian jump systems (PSMJSs) with mode-dependent derivative-term coefficient. Different from the existing results, the condition on stochastic stability of PSMJSs associated with state jumps behavior at switching instants is given by means of linear co-positive Lyapunuov function. On the basis of it, the conditions on stochastic stability under the cases of partially known transition rates and uncertain transition rates have been presented, respectively. All obtained conditions can be solved by linear programming (LP) technique. Finally, an example is introduced to illustrate the effectiveness and the merits of the results proposed in this article. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of observers and dynamic output-feedback controllers for positive linear systems with interval uncertainties. The continuous-time case and the discrete-time case are both treated in a unified linear matrix inequality (LMI) framework. Necessary and sufficient conditions for the existence of positive observers with general structure are established, and the desired observer matrices can be constructed easily through the solutions of LMIs. An optimization algorithm to the error dynamics is also given. Furthermore, the problem of positive stabilization by dynamic output-feedback controllers is investigated. It is revealed that an unstable positive system cannot be positively stabilized by a certain dynamic output-feedback controller without taking the positivity of the error signals into account. When the positivity of the error signals is considered, an LMI-based synthesis approach is provided to design the stabilizing controllers. Unlike other conditions which may require structural decomposition of positive matrices, all proposed conditions in this paper are expressed in terms of the system matrices, and can be verified easily by effective algorithms. Two illustrative examples are provided to show the effectiveness and applicability of the theoretical results. Index Terms--Dynamic output-feedback, interval systems, linear matrix inequalities (LMIs), positive observers, positive systems, uncertain systems.

This study addresses the positive filter design problem for continuous‐time positive Markov jump linear systems (PMJLSs). Based on the necessary and sufficient condition for L1 ‐gain performance, two sufficient conditions to design positive full‐order and reduced‐order L1 ‐filters for PMJLSs are provided in terms of linear programming, respectively. A practical numerical example of an isotropic, homogeneous and unidimensional aquifer is presented at last to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

This study introduces a problem of positive L1 filter design for positive piecewise homogeneous Markovian jump Takagi–Sugeno (T–S) fuzzy systems. The difference between the existing achievements is that the considered transition rate of the positive Markovian jump system is time‐varying. This time‐varying nature is finite piecewise homogeneous. The time variation of the transition rate is characterised by two cases: stochastic variation and arbitrary variation. First of all, sufficient conditions are obtained for stochastic stability and L1 performance under the transition rate in a manner of stochastic variation and arbitrary variation by means of choosing a linear co‐positive Lyapunov function. Then, based on the obtained achievements, the problem of positive L1 filter design for the positive piecewise homogeneous Markovian jump T–S fuzzy system is studied. All the mentioned problems in this study can be solved by linear programming. Finally, a biological model is proposed to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of reachable set estimation for discrete-time switched positive systems under two possible classes of exogenous disturbance. The multiple linear copositive Lyapunov function approach is applied to determine the bounding hyper-pyramids for the reachable set. Based on some Lyapunov-based inequalities and the linear version of the S-procedure technique, the bounding hyper-pyramids for the reachable set can be determined by solving a set of inequalities. Two optimisation methods are adopted to make the bounding hyper-pyramids as small as possible. Genetic Algorithm (GA) is utilised to search for the optimal value of the decision variables in the obtained inequalities. Finally, numerical examples are given to illustrate the effectiveness of the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper addresses the stochastic stability problem of positive Markov jump linear systems (PMJLSs). A necessary and sufficient condition of stochastic stability for PMJLSs is given which can be checked by solving linear programming feasibility problems due to the positivity property. A common co-positive Lyapunov function is constructed to solve the problem, and the equivalence among stochastic stability, 1-moment stability and exponential mean stability is proved afterwards. Considering the uncertain transition rates situation, PMJLSs with partially known transition rate matrix are investigated, and a necessary and sufficient condition for robust stochastic stability is proposed in linear programming form. Numerical examples are presented to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper presents a positive L 1 state-bounding observer which can estimate the state all the time for nonlinear positive Markovian jump systems. The considered system is represented by Takagi–Sugeno(T–S) fuzzy system. First of all, by constructing a linear co-positive Lyapunov function, the sufficient condition is obtained for stochastic stability and L 1 performance analysis respectively. Furthermore, a positive L 1 state-bounding observer for positive T–S fuzzy Markovian jump systems is designed. The conditions can be solved by linear programming. Finally, the results obtained are applied to the epidemiological model and illustrated to be better than the existing results by a numerical example. [ABSTRACT FROM AUTHOR]

This study is concerned with H ∞ control problems for positive systems with time delays using dynamic output feedback. Novel bounded real lemma for continuous‐time systems with time delays is first presented, which shows one of the remarkable properties of diagonal positive definite matrix solutions to linear matrix inequalities for positive systems. The proposed results reveal that H ∞ norms of positive systems with time delays in state and output equations are equivalent to that of the corresponding systems with zero delays. The positivity preserving H ∞ control problem by means of dynamic output feedback is also considered, and thus necessary and sufficient conditions in the forms of matrix equalities are established for the solvability of such problem. The desired controller gains can be obtained by means of cone complementarity linearisation techniques. A numerical example is finally given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the absolute and robust stability for a class of neutral-type Lur'e systems with an interval time-varying delay and sector-bounded nonlinearity. By discretising the delay interval into two segmentations with an unequal width, new delay-dependent sufficient conditions for the absolute and robust stability of neutral-type Lur'e systems are proposed in terms of linear matrix inequalities (LMIs) by employing a modified Lyapunov-Krasovskii functional (LKF). These conditions reduce the conservativeness in computing the maximum allowed delay bounds (MADBs) in many cases. Finally, several standard numerical examples are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper deals with a synchronization problem of a class of neutral-type complex dynamic networks with interval time-varying coupling delays under a pair of nonlinear constraints. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities ( LMIs) based on a modified Lyapunov- Krasovskii ( LK) functional approach. By a convexity analysis of the matrix function, a free-weighting matrix method is employed for the purpose of reducing the conservatism of the existing results. Two illustrative examples are given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The present aimed to study if porcine circovirus type 2 (PCV2), which adhered to zona pellucida (ZP), was able to enter mature porcine oocytes with intact and damaged ZP. Four groups, including uninfected ZP-intact oocytes (UOZI), uninfected ZP-damaged oocytes (UOZD), PCV2-infected ZP-intact oocytes (POZI), and PCV2-infected ZP-damaged oocytes (POZD) were studied. The oocytes were incubated with 1 mL minimum essential medium, containing 3.1 × 10 8 copies of PCV2 DNA for 1 hour. Mechanical procedure of the insertion by microneedle induced injuries to the ZP of porcine oocytes. At the blastocyst stage, the percentage of PCV2-infected embryos and the ratio of viral antigen-positive cells per embryo were determined by indirect immunofluorescence. To assess the effect of ZP injury on the developmental competence and quality of porcine PCV2-infected oocytes after parthenogenetic activation, blastocyst formation rates and terminal deoxynucleotidyl transferase–mediated deoxyuridine triphosphate nick-end labeling staining were analyzed. Moreover, real-time polymerase chain reaction was used to evaluate the expression of genes related to apoptosis and pluripotency at different developmental stages. The results of indirect immunofluorescence showed that only POZD group presented PCV2-infected embryos and viral-positive cells. The blastocyst rate of POZD group dropped down to approximately half of POZI group's (7.1 ± 1.5 vs. 14.5 ± 3.3). At the blastocyst stage, ZP injury increased apoptotic index of PCV2-infected embryos. The relative expression levels of Caspase 3 were higher in POZD group than the ones in POZI group at the two- and four-cell stages (not statistically significant). Compared with the one in POZI group, the ratio of antiapoptotic Bcl-xl gene to proapoptotic Bax gene, an indicator of the ability to resist apoptosis, was lower in POZD group at the one-cell stage, but higher at the two- and four-cell stages. Expression levels of Oct4 and Nanog associated with pluripotency were lower in POZD group than the ones in POZI group at the morula stage (not statistically significant). Noteworthily, the expression of Nanog was significantly lower in POZD group versus POZI group (P < 0.05), whereas relative expression of Oct4 was significantly higher in the former at the blastocyst stage (P < 0.01). In conclusion, PCV2, which attached to ZP, was able to enter mature porcine oocytes with damaged ZP and subsequently reduced the developmental competence and quality of the oocytes after parthenogenetic activation. [ABSTRACT FROM AUTHOR]