Discrete-time Switching Systems Research Articles

Improved results of asynchronous mixed [formula omitted] and passive control for discrete-time linear switched system with mode-dependent average dwell time

This paper primarily discusses the hybrid H∞ and passive control problems of asynchronous discrete-time switching systems based on mode-dependent average dwell time. In the process of analysis, we divide the running time of the subsystem into two cases: matching and not matching the controller. Firstly, we employ the method of mode-dependent average dwell time to model the system and derive a suitable switching signal, ensuring the system is global uniform asymptotic stability. Meanwhile, the weighted hybrid H∞ and passivity are achieved. Then, according to the different performance parameters of each subsystem, the appropriate controller is designed using the form of linear matrix inequalities to improve the stability of the system. Finally, the effectiveness of the proposed method is demonstrated by a numerical example and a population ecosystem.

Extended Mode-Dependent Persistent Dwell-Time Switching With Multi-Stage Dependent Modification or Averaging for Discrete-Time Switched Systems

In this brief, extended mode-dependent persistent dwell-time (EMDPDT) switching with the slow-and fast-switching areas of the mode-dependent feature, where subsystems separately run for not less and less than the MDPDT, is presented for a class of discrete-time switched systems (DTSSs). The existing MDPDT is shown to be a special case of the proposed EMDPDT. Further, to loosen the dwell-time restriction on slow-switching areas in the original MDPDT regularity, two novel principles of multi-stage dependent modification (MSDM) and multi-stage dependent averaging (MSDA) are launched. By means of MSDM (or MSDA), stability criteria are supplied for DTSSs under the EMDPDT switching, where smaller MDPDT lower bounds can be achieved for non-first stages (or partially random stages) in divided units formed by multiple stages. Meanwhile, at the cost of computation consumption, MSDM allows a lower total dwell-time restriction than MSDA. Finally, the efficiency and flexibility of EMDPDT with MSDM/MSDA are illustrated by an inverter example, which indicates the predictable applicability of the presented switching for practical switched applications.

Discrete-Time Switching Systems as Difference Inclusions: Deducing Converse Lyapunov Results for the Former From Those for the Latter

Nonlinear discrete-time switching systems under mode-dependent switching and dwell-time constraints are modeled by difference inclusions. Novel proofs of converse Lyapunov results are obtained for the switching systems as consequences of a converse Lyapunov result for a difference inclusion.

Stability Analysis for Digital Redesign of Discrete-Time Switched Systems Using H∞ Linear Matrix Inequality

In this paper, the stability problem for the digital redesign of discrete-time switched systems using H∞ linear matrix inequality (LMI) is investigated. We propose the switching time approach for digital redesign between controller work and failure, and this switching time will limit the system output within the system capacity. When the controller fails, the overall system will be unstable. Therefore, if the digital redesign controller is not restored in a certain period of time, the system output will exceed the system capacity. To solve this problem, we propose a switching law to determine the switching time between the stable mode (controller work) and the unstable (controller failure) mode; this will limit the overall system states in the unstable mode. In addition, the digital redesign controller has the advantage of faster tracking. After we propose a discrete-time switching system with stable and unstable modes, we use H∞ linear matrix inequality (LMI) and Lyapunov functions to prove the stability in detail. Finally, the numerical example illustrates the feasibility of the proposed approach.

Stable Near-Optimal Control of Nonlinear Switched Discrete-Time Systems: An Optimistic Planning-Based Approach

Originating in the artificial intelligence literature, optimistic planning(OP) is an algorithm that generates near-optimal control inputs for generic nonlinear discrete-time systems whose input set is finite. This technique is therefore relevant for the near-optimal control of nonlinear switched systems for which the switching signal is the control, and no continuous input is present. However, OP exhibits several limitations, which prevent its desired application in a standard control engineering context, as it requires for instance that the stage cost takes values in [0,1], an unnatural prerequisite, and that the cost function be discounted. In this paper, we modify OP to overcome these limitations, and we call the new algorithm OPmin. New near-optimality and performance guarantees for OPmin are derived, which have major advantages compared to those originally given for OP. We also prove that a system whose inputs are generated by OPmin in a receding-horizon fashion exhibits stability properties. As a result, OPmin provides a new tool for the near-optimal, stable control of nonlinear switched discrete-time systems for generic cost functions.

Observer-based quantized control for discrete-time switched systems with infinitely distributed delay

This paper studies the globally almost surely exponential stabilization of discrete-time switched systems (DSSs) with infinitely distributed delay. On account of the limitation of communication resources in the actual environment, a novel class of observer-based quantized control scheme is designed that incorporates the quantization of three kinds of signals: the measurement output, the state of observer, and the measurement output of observer. By employing S-procedure and some matrix inequality techniques, an algorithm is given to design the controller parameters. To reduce the conservativeness of the obtained results, new multiple Lyapunov–Krasovskii functionals (LKFs) with negative terms are proposed to deal with the infinitely distributed delay and mode-dependent average dwell time (MDADT) switching based on transition probability (TP) is introduced to study the stabilization of DSSs with both stable and unstable modes. It is worth highlighting that the improved stabilization conditions for DSSs can release the restriction on the length of dwell time (DT) of stable and unstable subsystems. Finally, a simulation example is presented to demonstrate the validity of the proposed method.

Passivity and Reduced-order Feedback Passification of Discrete-Time Switched Systems with Mode-Dependent Persistent Dwell Time

Passivity and Reduced-order Feedback Passification of Discrete-Time Switched Systems with Mode-Dependent Persistent Dwell Time

On Lyapunov Methods for Nonlinear Discrete-Time Switching Systems With Dwell-Time Ranges

A novel Lyapunov methodology for the stability check of nonlinear discrete-time switching systems, equipped with switches digraphs and nonuniform dwell-time ranges, is here presented. The novelty of the methodology consists in the following coexisting features: i) the global uniform (with respect to compact sets of initial conditions and switching signals) asymptotic stability is addressed; ii) the information on allowed switches and (nonuniform) dwell-time ranges is fully exploited; iii) no assumption is introduced on either stability or instability of the subsystems; iv) no assumption is introduced on the regularity of the functions describing the dynamics; v) the number of involved Lyapunov functions is always equal to the number of different modes; vi) a set of Lyapunov inequalities is uniquely defined coping with all scenarios of allowed switches and dwell-time ranges; vii) the provided Lyapunov conditions are necessary and sufficient for the global uniform asymptotic stability. Linear matrix inequalities obtained by this methodology are shown for the linear case.

Template-Dependent Lifts for Path-Complete Stability Criteria and Application to Positive Switching Systems

In the framework of discrete-time switching systems, we analyze and compare various stability certificates relying on graph constructions. To this aim, we define several abstract expansions of graphs (so-called lifts), which depend on the chosen family of candidate Lyapunov functions (the template). We show that the validity of a given lift is linked with the analytical properties of the template. This allows us to generate new lifts, and as a byproduct, to obtain comparison criteria that go beyond the concept of simulation recently introduced in the literature. We apply our constructions to the case of copositive linear norms for positive switching systems, leading to novel stability criteria that outperform the state of the art. We provide further results relying on convex duality and we demonstrate via numerical examples how the comparison among different stability criteria is affected by the properties of the copositive norms template.

State-Estimator-Based Asynchronous Repetitive Control of Discrete-Time Markovian Switching Systems

This paper investigates the problem of asynchronous repetitive control for a class of discrete-time Markovian switching systems. The control goal is to track a given periodic reference without steady-state error. To achieve this goal, an asynchronous repetitive controller that renders the overall closed-loop switched system mean square stable is proposed. To reflect realistic scenarios, the proposed approach does not assume that the system modes are available synchronously to the controller but instead designs a detector that provides estimated values of the system modes to the controller. Based on a detected-mode-dependent estimator, the plant and asynchronous repetitive controller are formulated as a closed-loop stochastic system. By utilizing tools from stochastic Lyapunov–Krasovskii stability theory, we develop sufficient conditions in terms of linear matrix inequalities (LMIs) such that the closed-loop system is mean square stable and also simultaneously establish a synthesis procedure for obtaining the gain matrices. We provide numerical simulations on an electrical circuit switched system to illustrate the approach.

ISS Small-Gain Theorem for Networked Discrete-Time Switching Systems

Abstract In this paper it is proved that a networked discrete-time switching system, equipped with a given switches digraph, is input-to-state stable, provided that there exist multiple Lyapunov functions (one for each mode) for each subsystem in the network, satisfying suitable standard inequalities, and provided that a set of suitable vector small-gain conditions are satisfied. The small-gain theorem here provided for the input-to-state stability takes into account the switches digraph. That is, the less is the number of edges in the switches digraph, the less is the number of involved Lyapunov inequalities and small-gain conditions which, if satisfied, guarantee the input-to-state stability of the entire switching system under study. The multiple Lyapunov functions for the entire system, guaranteeing the input-to-state stability, are determined by the multiple Lyapunov functions for each subsystem in the family. To the author’s best knowledge, this is the first paper in the literature concerning small-gain theorems for the input-to-state stability of nonlinear discrete-time switching systems with given switches digraphs.

A Switching System oriented Modeling and Control Strategy for Idle Speed Control of a Hybrid Powertrain

The market development of partially electrified powertrains in passenger cars motivates the re-consideration of the idle speed control problem. In this paper, a switching system model is first developed to unite the main discrete-event characteristics of the combustion engine and time-continuous characteristics of the electric motor. The presented model is classified as a discrete-time switching system model with linear subsystems.Based on this description, we further perform a model-based controller design using the lifting technique. Although the optimality property of the controller is bound to the assumption of constant turning speed, it still provides several useful properties. These are the inherent control allocation between electric and combustion engine, the consideration of the discontinuous behavior, and the discrete-time description basis which is important for implementation in a common controller architecture.

Cooperative control and communication of connected vehicles considering packet dropping rate

ABSTRACTThis paper investigates cooperative control and communication scheduling of a platoon of connected vehicles. Considering the effect of packet dropout and the network access limitation, the vehicular platoon is modelled as a discrete-time switching system. We obtain a set of sufficient conditions (where the rate of different platoon control modes is factored in) for string stability and schedulability of the vehicular platoon. A unified framework of network access scheduling and platoon control is proposed, which can guarantee string stability of the platoon of vehicles and resolve network access conflicts among them. Both numerical simulations and experimental studies with laboratory-scale cars have demonstrated the effectiveness of the presented co-design algorithm.

Composite nonlinear feedback design for discrete-time switching systems with disturbances and input saturation

ABSTRACTThis paper addresses the problem of robust controller design for a class of discrete-time switching systems with input saturation. To this aim, the composite nonlinear feedback method is extended to design a robust controller with improved performances in terms of the response speed and overshoot in the presence of disturbances and input saturation. The proposed approach is theoretically analysed and its closed-loop stability is proved. Then, the performance of the proposed method is verified using numerical simulations.

Switching-iterative learning control method for discrete-time switching system

In this paper, we propose a new monotonically convergent switching iterative learning control for a class of linear discrete time switched system. It is assumed that the considered switched systems are operated during a finite time interval repetitively, and then the iterative learning control scheme can be introduced. After the switched system is transformed into a 2D repetitive system, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived by using a Lyapunov functional approach and a quadratic performance function. It is shown that if certain LMIs are met, the tracking error $$l_2$$ norm converges monotonically to zero between (subsystem/iteration), while the switching learning gains could be determined directly by solving the LMIs.The integrated design of this SILC scheme is transformed into a robust monotonic stabilizability problem (RMS) of an uncertain switched system. A numerical simulation example is established shown the effectiveness of the proposed method .

Constructive stability and stabilizability of positive linear discrete-time switching systems

We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. This class generalizes the class of systems with independently switching state vector components. The distinctive feature of this class is that, for any system from this class, its components or blocks can be arbitrarily connected in parallel or in series without loss of the `constructive resolvability' property. It is shown also that, for such systems, it is possible to build constructively the individual positive trajectories with the greatest or the lowest rate of convergence to the zero.

Incremental Passivity and Incremental Passivity-Based Output Regulation for Switched Discrete-Time Systems.

This paper investigates incremental passivity and output regulation for switched discrete-time systems. We develop the results in two parts. First of all, a concept of incremental passivity is proposed to describe the overall incremental passivity property of a switched discrete-time system in the absence of the classic incremental passivity property of the subsystems. A condition for incremental passivity is given. A certain negative output feedback is designed to produce asymptotic stability. Incremental passivity is shown to be preserved under feedback interconnection. The second part of this paper is concerned with an application of the incremental passivity theory to the output regulation problem for switched discrete-time systems. The key idea is to construct a switched internal model with incremental passivity, which closely links the solvability of the output regulation problem. A characteristic of the switched internal model is that it does not necessarily switch synchronously with the controlled plant, which greatly increases the freedom of design. Once such a switched internal model is established, the output regulation problem is then solved by construction of the feedback interconnection between the controlled plant and the switched internal model. The main usefulness of the strategy is to get rid of the solvability of the output regulation problem for the subsystems.

Stability of discrete-time switching systems with constrained switching sequences

We introduce a novel framework for the stability analysis of discrete-time linear switching systems with switching sequences constrained by an automaton. The key element of the framework is the algebraic concept of multinorm, which associates a different norm per node of the automaton, and allows to exactly characterize stability. Building upon this tool, we develop the first arbitrarily accurate approximation schemes for estimating the constrained joint spectral radius ρˆ, that is the exponential growth rate of a switching system with constrained switching sequences. More precisely, given a relative accuracy r>0, the algorithms compute an estimate of ρˆ within the range [ρˆ,(1+r)ρˆ]. These algorithms amount to solve a well defined convex optimization program with known time-complexity, and whose size depends on the desired relative accuracy r>0.

Fault Detection for Switching Discrete-Time Systems with External Disturbance

This study addresses the robust fault detection problem for discrete-time switching systems under an arbitrary switching signal. Sufficient conditions building an observer are obtained by using multiple Lyapunov function and $${H}_{\infty }$$H? methods. A sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method.

A PD-Type Iterative Learning Control for a Class of Switched Discrete-Time Systems with Model Uncertainties and External Noises

A PD-type iterative learning control algorithm is applied to a class of linear discrete-time switched systems for tracking desired trajectories. The application is based on assumption that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily prespecified. By taking advantage of the super-vector approach, a sufficient condition of the monotone convergence of the algorithm is deduced when both the model uncertainties and the external noises are absent. Then the robust monotone convergence is analyzed when the model uncertainties are present and the robustness against the bounded external noises is discussed. The analysis manifests that the proposed PD-type iterative learning control algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily preset switching rules. The attached simulations support the feasibility and the effectiveness.