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This paper studies the problem of estimating the reachable set boundary of positive discrete-time systems with specific inputs in hyperspace. When the L 1 -norm or L ∞ -norm of the particular disturbance input to a positive linear discrete-time system is bounded by a constant, by using linear copositive Lyapunov functional method based on S-lemma, the reachable set could be constrained in a hyper-pyramid under some matrix inequality conditions. In an innovative way, by the method of directly calculating the dynamic trajectories of the system state, the reachable set can also be constrained in a hyper-rectangle. The approach of shrinking the size of the reachable set region is also developed. Finally, the validity of the results obtained is verified by examples of passenger flow in and out of customs. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of event-triggered controller for positive Takagi-Sugeno (T-S) fuzzy systems with a random time-delay. The random time-delay is described as a Markov process. A controller switched at different event-triggered instant is proposed. By constructing a new event-triggered instant-dependent linear co-positive Lyapunov function, the design criteria of event-triggered controller is derived to ensure the positivity and stability of the closed-loop system. These criteria can be solved by linear programming (LP) technique. A positive lower bound on the inter-execution time is ensured, which means that there is Zeno-free phenomenon. Finally, the simulation has demonstrated the effectiveness and merit of the proposed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the determination of positively invariant polyhedron for positive linear systems subject to external disturbances whose (∞, 1)-norm or (∞, ∞)-norm are bounded by a prescribed constant. Necessary and sufficient conditions for the existence of a positively invariant polyhedron are derived in terms of a set of inequalities which can be solved by linear programming, and the link between Lyapunov stability and positively invariant polyhedron is also revealed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the robust stability of uncertain neutral-type Lur'e system with time-varying delays and sector bounded nonlinearities. By constructing a modified Lyapunov-Krasovskii functional (LKF), some new robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) without using the general free-weighting matrix method. The criteria are less conservative and more efficiently calculative than some previous ones. Four numerical examples are presented to show the effectiveness and merits of the proposed approach. [ABSTRACT FROM AUTHOR]

• A new cost function is exploited. • The guaranteed cost control problem for T-S fuzzy NCSs with multiple quantizations is investigated. • An additional nonlinear term is employed in the control scheme. This paper researches the robust guaranteed cost (GC) control problem for a class of networked Takagi–Sugeno (T-S) fuzzy systems with local nonlinear segments and multiple quantizations, where the multiple quantizations mean that both the control input and the state are quantized through diverse dynamic quantizers. Three aspects are taken into account to perform the present study in depth. Firstly, the multiple quantizations case is investigated. Second, a novel cost function is exploited to perform the GC analysis issue, which consists of the quantized state and quantized control input. At last, a new control scheme is developed to fulfill the design of GC controller, where an additional nonlinear term is also employed besides the quantized state. By introducing auxiliary scalars and matrices, new conditions with regard to designing the dynamic quantizers and robust GC controllers are derived, which are expressed as a set of linear matrix inequalities (LMIs). Finally, a practical example is provided to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with positivity and stochastic stability of a class of positive singular Markovian jump time-delay systems with partially unknown transition rates. First, a necessary and sufficient condition is established to check the positivity of singular Markovian jump time-delay systems. By constructing an appropriate linear co-positive Lyapunov–Krasovskii function, a sufficient condition of stochastic stability for positive singular Markovian jump time-delay systems is established, which can be solved in terms of linear programming. Based on the results obtained, we give a necessary and sufficient condition of stability for normal positive Markovian jump systems and build some relationships with some existing results. Finally, three numerical examples are used to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus of discrete-time positive multi-agent systems. A framework on the consensus of positive multi-agent systems is constructed. By introducing a finite point and a self-feedback term, a novel consensus protocol is proposed to drive all states to common nonnegative finite values. An improved error model is established for positive multi-agent systems. Based on the consensus error model, the consensus of the agents is transformed into the stability of the error systems. Under the proposed consensus protocol and the new consensus error model, the consensus of agents is realized. A copositive Lyapunov function is chosen to derive the consensus of the multi-agent systems. Such a consensus approach is extended for time-delay multi-agent systems. All positivity and consensus conditions can be solved by virtue of linear programming. The main novelties of this paper lie in that: (i) A novel consensus error model is established, (ii) A finite value consensus is achieved, and (iii) Linear programming-based conditions are presented for the consensus design. Finally, two illustrated examples are given to verify the validity of the theoretical findings. • A novel consensus error model is established for PMASs. • A finite value consensus is achieved under the presented consensus framework. • Linear programming and copositive Lyapunov function are chosen as the computation and analysis approaches. [ABSTRACT FROM AUTHOR]

In this paper, the problem of global adaptive output feedback tracking is considered for a class of highly nonlinear time-delay systems with unknown control coefficient and relaxed lower-triangular growth constraints. Based on the non-separation principle, a non-identifier-based adaptive output feedback controller is proposed by designing a novel update law of the dynamic gain in observer and controller. The novel gain can simultaneously compensate the uncertain parameters, the output-polynomial growth rate and the unknown time-varying delay. The proposed controller is well universal attributed to using the non-identification adaptive mechanism, and all design parameters are easy to get by simple calculation. With the help of Lyapunov–Krasovskii functionals and Barbalat's lemma, it is shown that the solutions of the resulting closed-loop system are globally uniformly ultimately bounded by improving the backstepping design and dynamic high-gain scaling approach; the adaptive tracking is achieved under any small pre-given tracking error. Finally, the effectiveness of the proposed controller is illustrated by two examples. [ABSTRACT FROM AUTHOR]

This article aims to design proportional-derivative (PD) controllers for interval positive linear systems in the continuous-time domain, which still remains a widely-discussed open problem in positive systems theory. The specific objective is to design a PD controller for the system with interval uncertain parameters and time-varying delay, which simultaneously ensures closed-loop system stability and preserves positivity. The work proposes a systematic framework, with the aim of finding PD controller gains for positive robust stabilization. The methodology and algorithm are presented first in the study, and the performance of such methods is instantiated by numerical examples. [ABSTRACT FROM AUTHOR]