Analysis and Control of Switched Linear Systems Using Different Switching Strategies.

摘要

As a subclass of hybrid systems that exhibiting both continuous and discrete dynamics, switched systems typically consists of a family of differential/difference equations and a rule that orchestrates the switching among them. Switched systems provide a useful mechanism to model complex dynamics that are subject to abrupt parameter variations and sudden changes of system configurations. Moreover, as an additional degree of freedom besides control laws, switching strategies can be utilized to improve system performance as seen in many engineering systems such as electronics, communication network, power systems, automobile and traffic control. Nevertheless, analysis and control design of switched systems are difficult and pose significant challenges for control researchers and engineers. This dissertation is dedicated to analysis and control design of switched linear systems using different switching strategies.;We first study the analysis and control problem of switched linear systems subject to actuator saturation under controlled switching. With a state-dependent switching strategy and linear differential inclusion (LDI) description of the saturated switched systems, both stabilization and output feedback control design problem are addressed. Initially, we proposed an approach based on polytopic differential inclusion (PDI) description of the saturated system. We then found two major drawbacks of this approach: 1) Computational cost grows drastically when the number of control inputs increases. 2) A conservative set mapping results in conservativeness in the synthesis conditions. Thus we proposed another approach based norm-bounded differential inclusion (NDI) characterization of the saturated system that performs better than the previous approach in these two aspects mentioned above.;We then investigate the inherent chattering behavior of the well-known state-dependent minimum switching strategy since chattering is undesirable in practice. To mitigate chattering, we developed a relaxed min-switching strategy based on the idea that switching is not forced whenever a different subsystem obtains the minimum of the Lyapunov function but held until the minimum of the Lyapunov function falls below the Lyapunov function of the active subsystem by certain margin. Based on this idea, a tunable parameter, which is related to how large the margin will be, is introduced into the switching rule. Consequently, stability analysis and control synthesis conditions are derived in terms of modified Lyapunov-Metzler inequalities.;The above mentioned relaxed min-switching strategy can effectively reduce the frequency of the switching. However, as a state-dependent switching strategy, it cannot guarantee how slow the switching can be in terms of the activation time of each subsystem. This motivates us to consider time-driven switching strategies. The so-called "dwell-time" and "average dwell-time" based switching strategies are the most popular time-driven switching strategies. Nevertheless, they are restricted to the class of switched systems with some or all stable subsystems. In view of this, a novel mixed state-dependent and time-driven switching strategy is developed for switched systems with all unstable subsystems. It guarantees the stability of the switched system with a sufficiently small dwell time by enforcing a decrement of the Lyapunov function at each switch. Moreover, it provides a more general framework of analyzing switched linear systems as it contains the min-switching and the relaxed min-switching as special cases when dwell-time is not concerned. When dwell-time is concerned, it eliminates the chattering behavior commonly observed in min-switching based designs.