Reachable set estimation for switched nonlinear positive systems with impulse and time delay

Abstract

This paper deals with the reachable set estimation for the continuous-time switched nonlinear positive systems with impulse, disturbance, and mixed time-varying delays under the average dwell time switching. Based on a method developed in positive systems, sufficient conditions are established such that all solutions of the system converge exponentially to a ball. Both the bound of the reachable set and the convergence rate are determined explicitly. Compared with the existing result, the average dwell time given in this paper is less conservative. Finally, numerical examples demonstrate the effectiveness of our results. K E Y W O R D S disturbance, impulse, reachable set estimation, switched positive system, time delay INTRODUCTIONNoting that absolute temperature, absolute potential, concentration of chemical reactants, and the number of biological insects are all taken nonnegative values, the corresponding dynamic systems can be described by positive systems. Positive systems are dynamic systems with positive constraints on state variables. 1 Switched positive system is composed of a series of positive subsystems and rules that determine the switching between subsystems. Stability analysis is a basic problem for switched positive systems. In recent years, due to the wide application of switched positive systems in many fields, many stability and stabilization results related to switched positive systems have been obtained in References 2-15. In many practical control systems, time delays are often encountered, such as environmental systems, chemical process systems, transmission systems, and so on. Time delay is often the source of the system instability and poor performance. [16][17][18][19] For the stability of positive systems with time delay, relevant studies show that the asymptotic stability is insensitive to constant and bounded time-varying delays. 20 Therefore, positive systems with time delay have attracted much attention in recent years.Impulsive phenomenon is prevailing in many fields which means a physical quantity suddenly changes in a short period of time and quickly returns to its initial state. Impulses which contribute to dynamics of systems have been applied to many practical problems such as satellite orbit transfer, electrical engineering, stability and synchronization of chaotic secure communication systems, and so on. In the past few years, the control and analysis of impulse systems have been one of the hot spots, and significant progress has been made in References 21-25.Reachable set is a set of all possible states of the system under specific constraints, which defines the range of system state in normal operation. Therefore, the estimation of the state reachable set boundary is of great significance for the analysis of system stability and the diagnosis of system faults. Reachable set estimation of continuous-time linear time-varying systems with bounded perturbations was studied in Reference 26. In Reference 27, the authors discussed reachable set estimation for continuous-time and ...

Three‐stage least squares‐based iterative estimation algorithms for bilinear state‐space systems based on the bilinear state estimator

“…To overcome this difficulty, inserting (12) into (15), (13) into (16), and (14) into (17), we have the following relations:…”

“…11 A deal of research has been conducted on the identification of linear systems, bilinear systems, 12,13 nonlinear systems 14,15 and time-delay systems. [16][17][18] However, the nonlinear terms in the bilinear model pose some challenges to bilinear system identification. During the past decades, the minimal order state observer and the stable state estimator were considered for bilinear systems, and their necessary conditions for the existence of observers were discussed, but the estimation error depended on the input of the systems.…”

“…A deal of research has been conducted on the identification of linear systems, bilinear systems, 12,13 nonlinear systems 14,15 and time‐delay systems 16‐18 . However, the nonlinear terms in the bilinear model pose some challenges to bilinear system identification.…”

Reachable set estimation and controller design for discrete‐time singularly perturbed systems with time‐varying delay

“…Up to now, the RSE approach has been used to analyze various systems, including switch systems, 17,18 singular systems, [19][20][21] neural networks, [22][23][24] and so forth. Among these, time delays are often considered when applying the analysis of the RSE since they are inescapable in many control systems and may influence their performance and stability.…”

State bounding for time-delay impulsive and switching genetic regulatory networks with exogenous disturbance

“…This method does not rely on the LKFbased technique, and meanwhile the properties of some special matrices including Metzler/nonnegative matrices are used to estimate the system state. Later, this approach is further developed to nonlinear systems [17], fuzzy systems [3], and hybrid systems [33,32].…”