Switching Law Design Research Articles

Stabilization analysis of the switched discrete-time systems using Lyapunov stability theorem and genetic algorithm

This paper attempts to investigate the stabilization and switching law design for the switched discrete-time systems. A theoretical study of the stabilization and switching law design has been performed using the Lyapunov stability theorem and genetic algorithm. The present results demonstrated that can be applied to cases when all individual subsystems are unstable. Finally, some examples are exploited to illustrate the proposed schemes.

Scheduling of Transmission Order for Systems With Shared Communication Medium

This paper considers scheduling of transmission order for a set of continuous linear systems with a shared sensor-to-controller channel. By transferring the channel allocation problem to the problem of switching law design for a switched system, different allocation schemes including state-dependent scheme, periodic allocation scheme and random allocation scheme are proposed.

Robust H∞ Control for Neutral Uncertain Switched Nonlinear Systems using Multiple Lyapunov Functions

This paper focuses on the problem of robust H∞ control for a class of switched nonlinear systems with neutral uncertainties via the multiple Lyapunov function approach. Uncertainties are allowed to appear in channels of state, control input and disturbance input. Conditions for the solvability of the robust H∞ control problem and design of both switching law and controllers are presented. As an application, a hybrid state feedback strategy is proposed to solve the standard robust H∞ control problem for nonlinear systems when no single continuous controller is effective.

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.

On stability of switched homogeneous nonlinear systems

In this paper, the problem of stability of switched homogeneous systems is addressed. First of all, if there is a quadratic Lyapunov function such that nonlinear homogeneous systems are asymptotically stable, a matrix Lyapunov-like equation is obtained for a stable nonlinear homogeneous system using semi-tensor product of matrices, and Lyapunov equation of linear system is just its particular case. Following the previous results, a sufficient condition is obtained for stability of switched nonlinear homogeneous systems, and a switching law is designed by partition of state space. In particular, a constructive approach is provided to avoid chattering phenomena which is caused by the switching rule. Then for planar switched homogeneous systems, an LMI approach to stability of planar switched homogeneous systems is presented. Similar to the condition for linear systems, the LMI-type condition is easily verifiable. An example is given to illustrate that candidate common Lyapunov function is a key point for design of switching law.

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable (While some switching models are probably unstabilizable), an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.

H-infinity control for cascade minimum-phase switched nonlinear systems

This paper is concerned with the H-infinity control problem for a class of cascade switched nonlinear systems. Each switched system in this class is composed of a zero-input asymptotically stable nonlinear part, which is also a switched system, and a linearizable part which is controllable. Conditions under which the H-infinity control problem is solvable under arbitrary switching law and under some designed switching law are derived respectively. The nonlinear state feedback and switching law are designed. We exploit the structural characteristics of the switched nonlinear systems to construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law. The proposed methods do not rely on the solutions of Hamilton-Jacobi inequalities.

Stabilization of a class of switched systems via designing switching laws

One state transformation is used to construct switching laws for a class of switched systems totally composed of unstable subsystems. Some sufficient conditions for determining the switching law, such that the system is asymptotically stable, are derived.