Zero dynamics of nonlinear control systems with symmetries are studied in this paper. It is shown that the zero dynamics of a symmetric system is also symmetric and admits a special form of cascade decomposition. A local zero dynamics is always possible to be extended to the semiglobal case. The relation between the zero dynamics and the quotient system is also discussed.

首次提出切换组合系统的概念，给出了使此系统渐近稳定的分散切换控制律的设计，研究了带有连续控制量的组合大系统采用分散混杂状态反馈稳定化问题。

研究了切换系统输入对状态的稳定性。在所有子系统都是输入对状态稳定的条件下，利用各子系统的KL函数和K函数构造出切换系统所需的KL 函数和K函数，从而给出了切换系统输入对状态稳定的充分条件。对于一类常见的切换系统，计算出保证输入对状态稳定性的切换停留时间的下界。所有结果都是构造性的。

A concept of similar structure for linear control systems is defined in this paper. Under the assumption that a Lyapunov function of a system is available, we present a method calculating Lyapunov functions of a family of systems possessing similar structure without solving Lyapunov equations.

Quadratic stability of a class of switched nonlinear systems is studied in this note. We first transform quadratic stability problem into an equivalent nonlinear programming problem. Then, we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using Karush-Kuhn-Tucker condition for nonlinear programming problems. The necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space, which is much easier to check.

H∞ stabilization problem for a class of linear systems with time-varying norm-bounded uncertainty is studied by means of hybrid state feedback strategy. Suppose that there exist finite candidate static state feedback controllers in a set of controllers, and none of the individual controller makes the systems stabilizable with H∞ disturbance attenuation. When the gain matrices of state feedback controllers are known, based on single Lyapunov function technique and convex combination condition, a switching law which makes the uncertain switched linear system stabilizable with H∞ disturbance attenuation is constructed. When the gain matrices of state feedback controllers are unknown, multiple Lyapunov function technique is employed to derive a sufficient condition for the uncertain switched linear systems to be stabilizable with H∞ disturbance attenuation. Moreover, the existence of two static state feedback control laws is given in terms of the solvability of two coupled linear matrix inequalities. Finally, a simuIation example illustrates the main results of this paper.

研究了一类非线性开关系统的二次稳定性问题。首先将系统的二次稳定性转化为等价的带约束非线性规划问题，给出了系统二次稳定的充分必要条件；然后利用Fritz John条件，将该充要条件转化为较易检验的以代数方程和不等式的解表示的代数条件，最后举例说明了该代数条件的使用。

A globally stabilizing controller for the cart}pendulum system is designed in this paper. The design procedure consists of three parts. First, find a neighborhood of the origin in which a locally stabilizing controller can be used. Second, construct a linear controller for the cart subsystem and steer the position and velocity of the cart to the origin. The last part is to design several classes of bang}bang controllers and a switching strategy which guarantee that the trajectory of the system starting from any initial condition enters, in finite times of switching, the neighborhood where the locally stabilizing controller is e!ective.

Uniform ultimate boundedness of a class of switched linear systems is studied. A switched linear system in this class consists of msubsystems, and none of the individual subsystems need to be stabilizable. The switched linear system is shown to be uniformly ultimately bounded for any pre-given bound if the union of individual controllable subspaces covers the entire state space. An algorithm for guaranteeing uniform ultimate boundedness is given to provide the design of continuous controllers and the switching strategy.

This paper is concerned with global stabilization of a class of cascade switched nonlinear systems with linear parts which are switched linear systems. When the linear parts have uniform normal form and are minimum phase, we use constant gain linear feedback of the state of the linear parts to stabilize the switched nonlinear systems. Global asymptotic stability of closed-loop systems under arbitrary switching laws is obtained by constructing common Lyapunov functions.