Chang Duan

Analysis and control of switched linear systems via dwell-time min-switching

Abstract This paper addresses analysis and switching control problems of switched linear systems. To this end, a mixed time-driven and state-dependent switching strategy is proposed. It guarantees an average dwell time even when all subsystems are unstable. The switching rule and its associated switching output feedback controllers are designed to stabilize the switched system and satisfy a weighted L 2 gain performance. The proposed analysis and switching control approach could refrain frequent switches commonly observed in min-switching based designs. The effectiveness of the proposed approach has been illustrated through a spherical inverted pendulum example.

Output-feedback control for switched linear systems subject to actuator saturation

This article is devoted to the output-feedback ℋ∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous- and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ℒ2 (ℓ2)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach.

Hybrid Switched Gain-Scheduling Control for Missile Autopilot Design

This paper presents a new hybrid switched gain-scheduling control method for missile autopilot design via dynamic output feedback. For controller design purpose, the nonlinear missile plant model is first converted to a switched linear fractional transformation system. Then, the new hybrid switched gain-scheduling autopilot is designed, which consists of a switching dynamic output–feedback linear fractional transformation controller and a supervisor enforcing a controller state reset at each switching time instant. The proposed hybrid control scheme is shown to provide a systematic yet simple framework for missile autopilot design. Specifically, the control synthesis conditions that guarantee weighted L2 stability performance are formulated in terms of a finite number of linear matrix inequalities, which can be solved effectively via convex optimization without parameter-space gridding. Furthermore, stringent controlled performance and strong robustness against parameter perturbations are achieved using t...

Almost output regulation of discrete-time switched linear systems

In this paper, we propose a new hybrid control approach for almost output regulation of a class of discrete-time switched linear systems with average dwell time (ADT). Both controlled plant and exosystem are described by switched linear systems. The proposed hybrid controller is constructed as a switching impulsive system, where the controller states will undergo impulsive jumps at each switching instant. By using the ADT technique incorporated with multiple quadratic Lyapunov functions, the hybrid synthesis conditions for almost output regulation with asymptotic stability and weighted ℋ∞ performance are formulated as a set of linear matrix equations and linear matrix inequalities (LMIs), which can be solved effectively. The proposed hybrid control method has been demonstrated through a numerical example.

New results on switched linear systems with actuator saturation

This paper further studies the analysis and control problems of continuous-time switched linear systems subject to actuator saturation. Using the norm-bounded differential inclusion description of the saturated systems and the minimal switching rule, a set of switched output feedback controllers is designed to minimise the disturbance attenuation level defined by the regional gain over a class of energy-bounded disturbances. The synthesis conditions are expressed as bilinear matrix inequalities, and can be solved by numerical search coupled with linear matrix inequality optimisation. Compared to the previous method based on polytopic differential inclusion, the proposed approach has good scalability and potentially renders better performance. Numerical examples are provided to verify the effectiveness of the proposed approach.

Switching control synthesis for discrete-time switched linear systems via modified Lyapunov-Metzler inequalities

This paper addresses the switching control synthesis problem of discrete-time switched linear systems. A particular class of matrix inequalities, the so-called Lyapunov-Metzler inequalities is modified to provide conditions for stability analysis and output feedback control synthesis under a relaxed min-switching logic. The switching rule combined with switching output feedback controllers are designed to stabilize the switched closed-loop system and satisfy a pre-specified ℓ2 gain performance. The proposed switching control approach is to reduce the high frequency switches commonly observed in min-switching strategy based designs. The effectiveness of the proposed approach is illustrated through a numerical example.

Dwell-time min-switching for discrete-time switched linear systems

This paper addresses analysis and switching control problems of discrete-time switched linear systems. A mixed time-driven and state-dependent switching strategy is proposed to guarantee an average dwell time even when all subsystems are unstable. The switching rule and its associated switching output feedback controllers are designed to stabilize the switched system and achieve a disturbance attenuation performance. The proposed analysis and switching control approach could refrain frequent switches commonly observed in min-switching based designs. The effectiveness of the proposed approach is illustrated through a numerical example.

Output Feedback Control for Continuous-Time Switched Linear Systems Subject to Actuator Saturation

This paper is devoted to output feedback ℋ∞ control problem for continuous-time switched linear systems subject to actuator saturation. Using minimal switching rule, nonlinear output feedbacks, expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional ℒ2 gains over a class of energy-bounded disturbances. The synthesis condition is further simplified and can be solved through efficient LMI optimizations. The proposed switched control approach is also illustrated by a simple example.Copyright

Robust Switched Filtering for Time-Varying Polytopic Uncertain Systems

This paper studies the problem of designing robust switched filters for time-varying polytopic uncertain systems. The synthesis conditions for a set of filters under a min-switching rule are derived to guarantee globally asymptotical stability with optimized robust H1 performance. Specifically, the conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by linear matrix inequality (LMI) optimization techniques. The proposed approach utilizes a piecewise quadratic Lyapunov function to reduce the conservativeness of robust filtering methods based on single Lyapunov function, thus better H1 performance can be achieved. Both continuous and discrete-time robust filter designs are considered. To simplify filter implementation, a method to remove redundancy in min-switching filter members is also introduced. The advantages of the proposed robust switching filters are illustrated by several examples. [DOI: 10.1115/1.4025027]