Analysis And Control On A Class Of Switched Linear Systems

This dissertation concerns with some issues related to the analysis and control of aclass of switched linear systems. The main contributions are summarized as follows:(1) By using orthogonality transform, we prove that a class of switched linearsystems, of which the state matrices of subsystems are canonical matrices, are asymptoticstable under arbitrary switching rule. Based on common Lyapunov function method, aclass of second order switched linear systems and the switched linear systems of which thestate matrices of subsystems are upper (lower) triangular matrices are proved to beasymptotic stable under arbitrary switching rule. A sufficient condition of stability isobtained for general switched linear systems based on of dwell time.(2) The chattering mode in the dynamic process of the unforced switched systems isinvestigated. The relations between the rotation directions of trajectory, the increase ordecrease the polar radius of trajectory, and the convergent chattering mode are revealed.Based on aforementioned results, sufficient conditions for chattering mode are proposed bydistinguishing between two cases: switching delay neglected and switching delayconsidered. Two formulas are shown for computing the switching angles as well as thepolar radius alteration after once chattering. The proposed results can be applied tostabilize unforced switched systems. Finally, we define the chattering mode for higherorder switched systems and presented a checking method.(3) Robust stabilization is researched for switched systems with time delay. Firstly,by multiple Lyapunov functions method, a state feedback control strategy is proposed torobustly stabilize the discrete switched systems with time delay under arbitrary switchingrule, and an iterative algorithm is presented to solve the nonlinear matrix inequalities in theproposed theorems. The dynamic output feedback approach is established to stabilize thediscrete switched systems with time delay under arbitrary switching sequence. Then by theapproach of average dwell time, we design state feedback control law combining withcircular switching sequence to robust stabilize switched delay systems with H_∞performance, and indicate the permissive bound of circular switching sequence. Finally,robust reliable control is concerned for continuous switched systems with time varyingdelay under a state-dependent switching rule. On the premise that the minimal dwell timeof subsystems is known, state feedback control law is designed by applying multipleLyapunov functions technique to guarantee the switched delay systems to be asymptoticstable in both cases that the actuators of the switched systems work properly or partiallybreak down. (4) Stabilization and enlargement of contract region is studied for switched linearsystems with input saturation. Based on common Lyapunov function as well as multipleLyapunov functions respectively, we investigate state feedback stabilization for theswitched liner systems with single input saturation, and propose the switching method forenlarging the contract region. Aiming at the switched systems composed by two secondorder subsystems, some characteristics of phase trajectory is analyzed and then utilized todesign state feedback control to globally stabilize the switched systems by us appropriateswitching. Finally, we research the robust stabilization of a class of switched inputsaturation systems of which the density functions of the unknown parameters are given. Analgorithm called randomized gradient algorithm is applied to solve the robust statefeedback controller. The convergence of the randomized gradient algorithm is proved.