Time-dependent Switching Signal Research Articles

Stability analysis of switching systems with all modes unstable based on a $ \Phi $-dependent max-minimum dwell time method

<abstract><p>This paper applies stable and unstable switching instants to study switching systems with unstable modes under time-dependent switching signals. A new Lyapunov function is proposed to study the properties of switching instant using different $ \Phi $-dependent max-minimum dwell time methods. After that, the global exponential stability conditions for nonlinear and linear switching systems are derived and stable switching is used to compensate for unstable switching and unstable modes. The relevant results are extended to the controller design of linear switching systems. Finally, a simulation verifies the effectiveness of the results of this paper.</p></abstract>

Fault Detection Filter Design and Optimization for Switched Systems with All Modes Unstable.

This problem of intelligent switched fault detection filter design is investigated in this article. Firstly, the mode-dependent average dwell time (MDADT) method is applied to generate the time-dependent switching signal for switched systems with all subsystems unstable. Afterwards, the switched fault detection filter is proposed for the generation of residual signal, which consists of dynamics-based filter and learning-based filter. The MDADT method and multiple Lyapunov function (MLF) method are employed to guarantee the stability and prescribed attenuation performance. The parameters of dynamics-based filter are given by solving a series of linear matrix inequalities. To improve the transient performance, the deep reinforcement learning is introduced to design learning-based filter in the framework of actor-critic. The output of learning-based filter can be viewed as uncertainties of dynamics-based filter. The deep deterministic policy gradient algorithm and nonfragile control are adopted to guarantee the stability of algorithm and compensate the external disturbance. Finally, simulation results are given to illustrate the effectiveness of the method in the paper.

Global exponential stability and [formula omitted] control of limit cycle for switched affine systems under time-dependent switching signal

In this paper, the stability analysis of continuous-time switched affine systems (CTSASs) is addressed via dwell time switching. The main purpose of this note is to design a time-dependent switching signal assuring the global exponential stability of a desire limit cycle (which is selected from a set of attainable limit cycles). By constructing a discretized Lyapunov function and using the linear matrix inequalities technique, a set of conditions in the framework of dwell time are designed. For CTSASs, the performance indexes of the system in this neighborhood cannot be analyzed because most of the proposed controllers drive the system trajectory into a small enough neighborhood. Differently, the technique proposed in this note leads the CTSAS’s trajectory to the limit cycle so that the resulting conditions can consider the weighted H∞ performance level of the system. More specifically, the design conditions can be applied to open-loop subsystems that are unstable. At last, a numerical example and a practical example are given to illustrate our method.

Adaptive tracking control of switched linear systems with multiple disturbance observers

This paper deals with model reference adaptive control for an uncertain switched linear system in the presence of disturbances in the state and control input based on time-dependent switching methods. A novel composite disturbance observer-based adaptive controller with adaptive laws is proposed in a tracking problem of uncertain switched linear system. First, two disturbance observers are proposed to estimate disturbances. Then, a hybrid switched adaptive controller based on state feedback and disturbance observers is designed. Thereafter, based on time-dependent switching signals included dwell-time (DT), average dwell-time (ADT), and the mode-dependent approaches of DT and ADT, a globally uniformly ultimately bounded stability of the closed-loop switched linear system is proved. Finally, the theoretic achievement is applied to a highly manoeuvrable aircraft technology vehicle to demonstrate the significance of the proposed method.

On Stabilizability of Switched Linear Systems Under Restricted Switching

This article deals with the stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys prespecified restrictions on switches between the subsystems and dwell times on the subsystems. We derive sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set of purely time-dependent switching signals that obeys the given restrictions. The main apparatuses for our analysis are (matrix) commutation relations between certain products of the subsystems matrices and graph-theoretic arguments.

Yet another matrix commutator condition for stabilizability of discrete-time switched linear systems

Abstract This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set of purely time-dependent switching signals that are allowed to activate all subsystems. The main apparatuses for our analysis are (matrix) commutation relations between certain products of the subsystems matrices and graph-theoretic arguments. We present a numerical experiment to demonstrate our results.

Stabilization of switched systems with time-dependent switching signal

The switched system with possible unstable modes is investigated by employing both stabilizing and destabilizing switching instants under the time-dependent switching signal. A new piece-wise Lyapunov function is proposed to distinguish the property of the switching instants with the help of dwell time information. Then, globally exponentially stable conditions of the switched nonlinear system and the switched linear system are derived, respectively, which compensate the state divergence resulted from unstable modes and destabilizing switching instants by stabilizing switching instants. The related result is extended to the controller design of the switched linear system. Besides, for the switched linear systems with pairwise commutative, a necessary and sufficient condition is proposed based on a new time-dependent switching signal, which provides a novel way for the controller design of the switched system. Finally, simulation is presented to show the effectiveness of our results.

Robust integral sliding mode control for uncertain switched systems under arbitrary switching rules

This article proposes a design of robust integral sliding mode control under arbitrary time-dependent switching rules for uncertain switched systems (SSs). First, a description of the control problem for the switched system is presented, after which a recursive searching method of the common Lyapunov function (CLF) for the robust stable matrix set is proposed. Based on the proposed CLF searching method, a common robust integral-type sliding mode surface is then designed, which is robust to the unmatched uncertainties. Consequently, a sliding mode controller is designed so that the system state remains on the sliding mode surface from the initial time instant. Finally, the correctness and performance of the proposed control design are verified through simulations. The controlled switched system with unmatched uncertainty in the sliding mode is robust stable under any time-dependent switching signal.

Stabilization of discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function

By introducing a class of weak switched linear copositive Lyapunov functions, this paper designs new time-dependent switching signals guaranteeing asymptotic stability of discrete-time switched positive linear systems whose subsystems are only marginally stable. Our results have advantages over some existing ones in the literature. Moreover, the main results have been extended to the general switched linear time-varying system with disturbance. Numerical examples well demonstrate the superiority of the obtained results.

Discrete-time switching MPC with applications to mitigate resistance in viral infections

Many engineering applications can be described as switched linear systems, in which the manipulated control action is the time-dependent switching signal. In such a case, the control strategy must select a linear autonomous system at each time step, among a finite number of them. Even when this selection can be done by solving a Dynamic Programming (DP) problem, the implementation of such a solution is often difficult and state/control constraints cannot be explicitly accounted for. In this paper, a new set-based Model Predictive Control (MPC) strategy is presented to handle switched linear systems in a tractable form. The optimization problem at the core of the MPC formulation consists of an easy-to-solve mixed-integer optimization problem, whose solution is applied in a receding horizon way. The medical application of viral mutation and its respective drug resistance is addressed to acute and chronic infections. The objective is to attenuate the effect of mutations on the total viral load, and the numerical results suggested that the proposed strategy outperforms the schedule for available treatments.

Exponential stabilization of switched time-varying systems with delays and disturbances

This paper deals with exponential stabilization for a class of switched time-varying systems. By taking time-varying delays and nonlinear disturbances into consideration, time dependent switching signals have been characterized in terms of Metzler matrices such that the resulting system is globally exponentially stable. Compared with preceding works, we introduce a model transformation and an approach without involving the Lyapunov-Krasovskii functional to derive new exponential stability criteria for switched time-varying systems under the average dwell time switching. Numerical examples show that the obtained theoretical results can be applied to some cases not covered by some existing results.

Stability analysis of discrete-time switched systems via Multi-step multiple Lyapunov-like functions

In this paper, we propose a Multi-step multiple Lyapunov-like functions (MLFs) based approach to prove the stability and asymptotic stability of discrete-time switched systems under pre-given time-dependent switching signals. We start with the definition of Multi-step MLFs, which is a relaxation of traditional MLFs. Then, for a discrete-time switched nonlinear system (SNS) under a given time-dependent switching signal, several sufficient conditions for its stability and asymptotic stability are successively provided by using either Multi-step MLFs or strengthened Multi-step MLFs, respectively. Afterwards, for a discrete-time switched linear system with a special time-dependent switching signal, we derive two less conservative linear matrix inequality based criteria for demonstrating its asymptotic stability. In the end, three examples are given to illustrate the applicability and advantage of our relaxed results.

Finite-time stability of a class of continuous-time non-homogeneous switched systems

This paper is concerned with the finite-time stability problem of a class of linear continuous-time non-homogeneous switched systems under a time-dependent switching signal constrained by a dwell-time T. Once the finite-time stability is guaranteed, one of the main results of the paper guarantees that any system trajectory starting in a subset Ω1 of the state-space will remain in Ω2⊃Ω1 over a finite time interval and for any switching sequence with a dwell-time T̄≥T. The finite-time stability conditions are provided in the form of bilinear matrix inequalities (BMIs), which can be transformed to linear matrix inequalities (LMIs) by means of a step-by-step procedure that includes the computation of the sets Ω1 and Ω2 by the knowledge of the system operating range. Three illustrative examples are used to show the validity of the results.

Practical stability of switched systems without a common equilibria and governed by a time-dependent switching signal

In this paper, the problem of practical stability of some classes of continuous-time switched systems is studied. The main results of this paper include some sufficient conditions concerning practical stability of continuous-time switched nonlinear systems without a common equilibria for all subsystems. In this class of switched systems, the equilibrium point varies discontinuously according to a time-dependent switching signal. So, stability with respect to a set, rather than a particular point, is discussed. Using this preliminary result, we present sufficient conditions in the form of linear matrix inequalities (LMIs) for practical stability of a particular class of switched systems without common equilibria: the switched affine systems. An illustrative example in the power system stability area is presented to show the validity of the results.

Control of switched linear systems with actuator saturation and its applications

Many practical control systems can be modeled as switched linear systems with stabilizable and unstabilizable subsystems. In this paper, control synthesis for such a class of systems with actuator saturation is well investigated in the continuous-time and discrete-time cases. Based on the time-dependent switching signals and multiple Lyapunov function method, stabilization conditions are established in terms of LMIs. To obtain an attractive region as large as possible, the optimization problems are formulated. As the applications, the asynchronously switched control and intermittent control under actuator saturation are discussed. Numerical examples and simulations are presented to illustrate the feasibility and values of the proposed results.

Asymptotic Controllability by Means of Eventually Periodic Switching Rules

In this paper we introduce the notion of eventually periodic switching signal. We prove that if a family of linear vector fields satisfies a mild finite time controllability condition, and for each initial state there exists a time-dependent switching signal which asymptotically drives the system to the origin (possibly allowing different signals for different initial states), then the same goal can be achieved by means of an eventually periodic switching signal. This enables us to considerably reduce the dependence of the control law on the initial state. In this sense, the problem addressed in this paper can be reviewed as a switched system theory version of the classical problem of investigating whether, or to what extent, a nonlinear asymptotically controllable system admits stabilizing feedback laws.