Stable Subsystems Research Articles

Leader-following consensus of second-order multi-agent systems with time-varying delays and arbitrary weights

Using Lyapunov first method instead of traditional Lyapunov second method, this paper focuses on studying the consensus tracking control problem of multi-agent systems (MASs) with time-varying delays and arbitrary adjacent weights under fixed topology and switching topology, respectively. We first give four equivalent criteria for MASs with fixed communication topology, where the positive stability of matrix [Formula: see text] ( L is the Laplacian matrix of [Formula: see text], B is the leader’s adjacency matrix) not only plays a key role as usual but also becomes an urgent and more complicated problem due to the introduction of negative weights in MASs. Second, for MASs with switching communication topology if the average dwell time of switching topology, the total activation time of stable subsystems and the upper bound of time delay satisfy some conditions, then MASs with all stable subsystems (partially stable subsystems) can achieve consensus tracking. Finally, simulations are given to demonstrate the effectiveness of our theoretical results.

Методичні основи оцінки життєздатності підприємств

The purpose of the article is to substantiate the theoretical concepts and methodological bases for assessing the level of enterprise viability. Research methods. The basis to the formation of theoretical and methodological principles for assessing the viability of enterprises was a systematic approach. In the process of the research the dialectical means of perceiving the processes and phenomena were used, as well as the method of analysis (to determine the components of enterprise viability and relationships between them), the comparative method (to identify the common and different in the existing methods of assessing enterprise viability), the graphical method (to build a model of enterprise viability on the basis of sustainable development), the method of generalization (describing the stages of assessing the enterprise viability), the abstract-logical method (theoretical generalizations and formulation of conclusions). Research results. Based on the principles of sustainable development, the main three areas of the enterprise interaction with the external environment for the formation of its viability are identified: economic, social and environmental. Based on the analysis of existing approaches to assessing the enterprise viability, the main directions for assessing the viability are suggested, depending on the scope of interaction between the enterprise and the external environment. The stages of assessing the enterprise viability have been formed. Scientific novelty. The methodological bases for assessing the level of enterprise viability based on evaluating the stability of internal subsystems of the enterprise, its corporate culture, relations with internal and external partners, as well as environmental safety have been improved. Practical significance. The proposed methodological guidelines will help systematically and comprehensively assess the enterprise viability in terms of its internal and external environments, and will make it possible to perform a comparative analysis of the enterprise viability in the dynamics of a number of years or for different enterprises between them. Tabl.: 2. Figs.: 2. Refs.: 14.

Stability analysis of cyclic switched linear systems: An average cycle dwell time approach

In this paper, the stability problem of switched linear systems with a class of cyclic switching signals is investigated. Firstly, a new concept of average cycle dwell time (ACDT) is introduced to relax the conservativeness of cycle dwell time that is extensively used in the literature. In addition, the ACDT is further extended to stable cyclic switching sequence dependent average cycle dwell time (S-ACDT) and unstable cyclic switching sequence dependent average cycle dwell time (U-ACDT). Secondly, the stability criteria for cyclic switched linear (or nonlinear) systems with ACDT or both S-ACDT and U-ACDT are derived by resorting to a technique that uses multiple Lyapunov functions. Both cyclic switched linear systems and cyclic switched nonlinear systems which contain all stable subsystems or partly stable subsystems are studied. Finally, a numerical example is given to demonstrate the feasibility of the proposed techniques.

Stability and stabilisation of switched time-varying delay systems: a multiple discontinuous Lyapunov function approach

In this paper, stability and stabilisation of switched time-varying delay systems are investigated. By developing, a multiple discontinuous Lyapunov function approach and using the mode-dependent average dwell time (MDADT) switching signal, sufficient conditions are first proposed to guarantee the exponential stability of the switched system with stable and unstable subsystems where the time-varying delay is considered in the states. Relaxed stability conditions are also obtained by using a form of the Bessel–Legendre inequality. Then stabilisation of the proposed system is presented by designing a sliding mode controller. Sufficient conditions and sufficient relaxed conditions of a reduced-order sliding mode dynamics are derived, and desired sliding surfaces in the form of linear matrix inequalities (LMIs) are also given. The obtained conditions are checked by using the combined genetic algorithm and convex programming techniques. Moreover, some numerical and practical examples are given to illustrate the effectiveness of the obtained theoretical results.

Unified mode‐dependent average dwell time stability criteria for discrete‐time switched systems

SummaryIn this article, a unified mode‐dependent average dwell time (MDADT) stability result is investigated, which could be applied to switched systems with an arbitrary combination of stable and unstable subsystems. Combined with MDADT analysis method, we classified subsystems into two categories: switching stable subsystems and switching unstable subsystems. State divergence caused by switching unstable subsystems could be compensated by activating switching stable subsystems for a sufficiently long time. Based on the above considerations, a new globally exponentially stability condition was proposed for discrete‐time switched linear systems. Under the premise of not resolving the LMIs, the MDADT boundary of the new stability condition is allowed to be readjusted according to the actual switching signal. Furthermore, the new stability result is a generalization of the previous one, which is more suitable for the case of more unstable subsystems. Some simulation results are given to show the advantages of the theoretic results obtained.

Stability criteria for stochastic neural networks with unstable subnetworks under mixed switchings

In this paper, stability of a class of stochastic neural networks with switching signal is studied. Firstly, by means of the method of limiting average dwell time, we analyze the stability of switched systems which potentially contain unstable subsystems and stable subsystems simultaneously. Moreover, considering two types of switchings: stabilizing switchings and destabilizing switchings, we adopt time-dependent parameters to give a description of the relationship between two successive activated subsystems. Based on the obtained results for switched systems, some stability criteria for switched neural networks with stochastic disturbances are derived. At last, we present a numerical example to demonstrate the effectiveness of our results.

Event-triggered consensus control of high-order multi-agent systems with arbitrary switching topologies via model partitioning approach

This paper investigates the problem of event-triggered consensus control for high-order multi-agent systems with arbitrary switching topologies. To achieve this goal, a novel model partitioning approach is proposed, where the high-order error systems are partitioned into stable subsystems and unstable subsystems through coordinate transformations. By analyzing the unstable subsystems under arbitrary switching, an appropriate controller can be designed to guarantee the subsystems stable. Then the controller gain of the multi-agent systems can be derived through inverse transformations. The designed controller can guarantee the error state convergence under each topology within any time interval, which further ensures the consensus of high-order multi-agent systems under arbitrary switching topologies. Finally, a numerical example is provided to illustrate the feasibility of the theoretical results.

Weighted $$\mathbf{H}_\infty$$ Performance Analysis of Nonlinear Stochastic Switched Systems: A Mode-Dependent Average Dwell Time Method

In this paper, the issues about weighted $$H_\infty$$ performance analysis and $$H_\infty$$ control for the stochastic switched nonlinear systems (SSNSs) with multiplicative noise are investigated. The mode-dependent average dwell time (MDADT) method is used to deal with the switching in different modes. Firstly, we get a sufficient condition to show that the considered system with all stable subsystems achieves the exponential stability in mean square sense and a specified weighted $$H_\infty$$ performance, which is extended to the case that both stable and unstable subsystems coexist in terms of second-order Hamilton-Jacobi inequalities (HJIs). Then, by using Takagi-Sugeno (T-S) fuzzy approach, the $$H_\infty$$ controller for SSNSs is designed via solving a set of linear matrix inequalities (LMIs). Finally, an example is supplied to illustrate the effectiveness of our results.

Stabilization of switched positive system with impulse and marginally stable subsystems: A mode-dependent dwell time method

Abstract In this article, the problem of stabilization for the switched positive linear system (SPLS) with impulse and marginally stable subsystems is studied, in which both the continuous time case and the discrete time case are taken into account. By the usage of a piecewise weak linear copositive Lyapunov function (LCLF) and the mode-dependent dwell time (MDT), time-dependent switching control laws are designed to guarantee the asymptotic stability of the system. Furthermore, based on the comparison principal for positive systems, the main results are generalized to the time-variant SPLS. Two examples are worked out to indicate that our results have advantages over some known results in the literature.

Robust Adaptive Output Feedback Control for a Class of Underactuated Aerial Vehicles with Input and Output Constraints

This paper addresses the problem of nonlinear robust adaptive output feedback controller for a class of underactuated aerial vehicles with input and output constraints. To solve the problem, the modular design strategy is proposed for the control design. By using the neural networks (NNs) to approximate system uncertainties and observers to reconstruct system states, robust adaptive output feedback controllers are developed. By using a combination of saturation functions and barrier functions, input and output constraints are simultaneously dealt with. The design methodology shows that a cascaded system of an input-to-state stable (ISS) subsystem driven by an ultimate bounded (UB) subsystem enjoys ultimate boundedness property. In addition, the tracking error converges to adjustable neighbourhoods of the origin.

Observer‐based stability of switched system under jamming attack and random packet loss

This study investigates the cyber-security control problem of a networked switched system. Firstly, a joint probabilistic model is utilised to characterise the communication failure caused by the jamming attack and random packet loss. Then the attention is focused on designing an observer based controller that can generate the control input using the last successfully received system output. After that, with the average dwell time scheme, sufficient conditions are derived to ensure the almost sure asymptotical stability of the overall-system with stable and unstable subsystems. In addition, an approach is developed to obtain the feasible solution of state feedback and observer gains. Finally, a simulation example implies the effectiveness of the authors' methods.

A novel control architecture for marginally stable dynamically substructured systems

Dynamic substructuring is a popular hybrid testing technique that mixes physical testing with numerical simulations. Research in this domain has mainly focused so far on structures and decomposition strategies that result in asymptotically stable systems. However, several cases fall outside this family, with either the physical or the numerical part being only marginally stable post-decomposition. A typical example of such scenario is when a mass is split between physical and numerical parts. For generic structures with marginally stable subsystems, current techniques often fail to deliver satisfactory performance or require modifications to the original structure. In this paper, analytical results – valid for generic structures – are derived to highlight the potential shortcomings of current techniques and to motivate the proposal for a novel control architecture to enable dynamic substructuring with marginally stable subsystems. By selecting a suitable set of signals for control design and by augmenting the control strategy via a local controller for the marginally stable subsystem, the proposed method allows accurate hybrid testing without relying on the modifications of the original structure that classical approaches require. This technique is suitable for all of the mass split structures, and indeed for all marginally stable structures, which means that the results are applicable to a wide range of hybrid testing problems. A simulated benchmark problem of hybrid testing for vibrating structures is included to demonstrate the effectiveness of the proposed technique.

Совершенствование технологического потока линии производства инстантированного киселя

Introduction. By 2030, Russia will have abandoned the export-dependent economy and moved on to the innovation-based development, as it is stated in the Long-Term Plan for Social and Economic Development of the Russian Federation issued by the Ministry of Economic Development. Improving the production of products reduces the cost of finished products and increases their biological value. Working population often fails to maintain a balanced diet. Therefore, it is necessary to develop products that contain a large number of biologically active substances, e.g. instant drinks of plant origin.
 Study objects and methods. The level of integrity of the technological production line for instant starch drinks depends on the level of integrity of each of its subsystems. By comparing the monitored parameters with the given values, one can assess the integrity level of the entire system. The subsystem that is responsible for the semi-finished product causes the greatest perturbation in the stability of the entire system. According to the theory of the technological flow proposed by Dr. V.A. Panfilov, this is subsystem B. The problem is associated with the instability of the granulation process, i.e. unstable particle size distribution in the finished product. The instability may occur due to the principle of operation and design features of dish-shaped granulators. As a result, the quality of the
 finished product decreases.
 Results and discussion. The team developed a new hardware design of a machine-hardware scheme for the production of instantiated granular food products (IGPP). They conducted a repeated assessment of the integrity level of the entire technological system. The analysis of the production technology of IHPP employed a systematic approach, which made it possible to determine the level of its organization and increase it. The positive changes took place after the introduction of a new subsystem of the solid-state mechanochemical activation of potato starch. The activation changed the physical and mechanical properties of native starches, thus intensifying the process of structure formation. In addition, the integrity of the entire subsystem could be increased by changing the principle of structure formation of granules. A new granulator and a new operating principle made it possible to perform granulation by pelletizing in controlled segregated flows. 
 Conclusion. The stability of subsystem B increased by 0.31, while the stability of the whole system increased by 0.56. The success was directly related to the new granulation technologies and a change in the technological flow of production of instant starch drinks.

Event-Triggered Stabilization of a Class of Nonlinear Time-Delay Systems

This article presents a solution to event-triggered stabilization of a class of nonlinear time-delay systems in the strict-feedback form. Set-valued maps are employed to handle the event-triggered sampling errors, and the closed-loop system is transformed into an interconnection of input-to-state stable subsystems through a set-valued constructive design. The event trigger is designed to satisfy a cyclic-small-gain condition, and the stability of the closed-loop event-triggered system is guaranteed by the cyclic-small-gain theorem for time-delay systems. The proposed design is verified by a practical example of cascade connected reactors.

Robust matrix commutator conditions for stability of switched linear systems under restricted switching

This article treats global uniform exponential stability (GUES) of discrete-time switched linear systems under restricted switching. Given admissible minimum and maximum dwell times, we provide sufficient conditions on the subsystems under which they admit a set of switching signals that obeys the given restrictions on dwell times and preserves stability of the resulting switched system. Our analysis relies on combinatorial arguments applied to matrix commutators. The proposed set of stabilizing switching signals is characterized in terms of duration of activation of Schur stable subsystems and non-consecutive activation of distinct unstable subsystems.

Global output feedback control for nonlinear cascade systems with unknown output functions and unknown control directions

SummaryThis paper investigates the output feedback control for the uncertain nonlinear system with the integral input‐to‐state stable (iISS) cascade subsystem, which allow not only the unknown control direction but also the unknown output function. The unknown output function only needs to have a generalized derivative (which may not be derivable), and the upper and lower bounds of the generalized derivative need not to be known. To deal with the challenge raised by the unknown output function and the unknown control direction, we choose a special Nussbaum function with a faster growth rate to ensure the integrability for the derivative of the selected Lyapunov function. Then, a dynamic output feedback controller is designed to drive the system states to the origin while keeping the boundedness for all other closed‐loop signals. Moreover, via some appropriate transformations, the proposed control scheme is extended to deal with more general uncertain nonlinear cascade systems with quantized input signals. Finally, two simulation examples are given to show the effectiveness of the control scheme.

Almost Sure Stability of Markov Jump Systems With Persistent Dwell Time Switching

This article investigates the exponential almost sure stability (EAS-stability) of switching Markov jump systems (SMJSs). The considered SMJSs are ruled by Markov jump switching and deterministic switching simultaneously. The deterministic switching follows the persistent dwell time (PDT) switching which is more general than the dwell time (DT) switching and the average DT (ADT) switching. To tackle the difficulties caused by PDT switching, a new method is constructed by restricting the deterministic switching frequency into a suitable range. First, the detailed parameter analyzing is presented because the general measure parameter is unable to describe the dynamic characteristic of SMJSs with PDT switching. Second, the switching rule is established on account of the restricted switching frequency. Two sufficient conditions are further proposed to ensure the EAS-stability of SMJSs with all stable subsystems and SMJSs containing unstable subsystems, respectively. A numerical example and a fault-prone system model are given to illustrate the effectiveness of the proposed strategies.

New Stability Conditions for Switched Linear Systems: A Reverse-Timer-Dependent Multiple Discontinuous Lyapunov Function Approach

In this article, the stability issues are addressed for switched linear systems (SLSs) with mode-dependent average dwell time (MDADT). By dividing the dwell time into several segments, and constructing a reverse timer which starts timing at the end of each segment, we propose a new reverse-timer-dependent multiple discontinuous Lyapunov function (RTDMDLF), which is more general than the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF). With the help of the RTDMDLF approach, several convex and nonconvex stability conditions are derived for SLSs with both stable and unstable subsystems, and the relation of these conditions and existing ones is revealed. Moreover, the stability conditions for SLSs with all stable subsystems are also given. All the results are presented in terms of infinite-dimensional linear matrix inequalities (LMIs), which can be relaxed into computable conditions by using a discretized approach. It is shown that the tighter bound of MDADT can be achieved by the RTDMDLF approach compared with those of the literature. Finally, the advantages of the results are illustrated within three numerical examples.

Lie-Algebraic Criterion for Stability of Switched Differential-Algebraic Equations

Abstract In this paper, we prove a Lie algebraic result for stability of switched DAEs with a common descriptor matrix (common E matrix). We first show that if a switched DAE with a common descriptor matrix is asymptotically stable, then it is also globally uniformly exponentially stable. We then show that switched DAEs with common descriptor matrix and consistent block upper triangular structure is globally uniformly exponentially stable if and only if the switched DAEs corresponding to the diagonal blocks are globally uniformly exponentially stable. Finally, we show that a switched DAE with common descriptor matrix, stable and impulse free DAE subsystems, is globally uniformly exponentially stable (GUES) if there exists an invertible matrix N such that the Lie algebra {N E, N Ai: i ϵ P}LA is solvable.

Decoupling of Discrete-time Dynamical Systems Through Input-Output Blending

This paper presents a subsystem decoupling method for Linear Time Invariant Discrete-time systems. The aim is to control a selected subsystem, while not affecting the remaining dynamics. The paper extends earlier continuous time results to discrete time systems over a finite frequency interval. Decoupling is achieved by suitable input and output blend vectors, such that they maximize the sensitivity of the selected subsystem, while at the same time they minimize the transfer through the undesired dynamics. The proposed algorithm is based on an optimization problem involving Linear Matrix Inequalities, where the H- index of the controlled subsystem is maximized, while the transfer through the dynamics to be decoupled is minimized by a sparsity like criteria. The present approach has the advantage that it is directly applicable to stable and unstable subsystems also. Numerical examples demonstrate the effectiveness of the method.