摘要
混杂系统是由离散事件动态系统与连续时间动态系统或离散时间动态系统相互混合、相互作用而形成的统一动态系统。混杂系统理论的提出既是社会经济发展的需要，也是计算机科学和控制科学发展的必然结果。
混杂系统具有十分复杂的动态特性。当系统参数存在不确定性时，系统的性能分析和控制变得非常困难，因此，给出混杂系统在参数不确定情况下的鲁棒性能分析和控制方法在理论和应用两方面都具有重要意义。
本文以混杂系统的Lyapunov稳定性理论为基础，采用线性矩阵不等式方法对参数不确定线性混杂系统的鲁棒稳定性分析、鲁棒镇定以及鲁棒性能综合这三个方面进行了深入研究，具体研究内容涉及以下五个方面：
(1)针对离散事件状态转移条件为状态依赖的参数不确定线性连续混杂系统，基于共同Lyapunov函数提出了此类混杂系统全局鲁棒渐近稳定的判定条件，并基于分段二次型Lyapunov，函数给出了这类混杂系统局部鲁棒Lyapunov稳定的充分条件。文中所得结果不仅适用于具有非周期离散事件状态切换序列的混杂系统，也适用于具有周期离散事件状态切换序列的混杂系统。
(2)针对离散事件状态转移条件为状态依赖的参数不确定线性离散混杂系统，基于共同Lyapunov函数给出了此类系统全局鲁棒渐近稳定判定条件，基于分段Lyapunov函数提出了一般离散混杂系统在Lyapunov意义下局部稳定判定定理，并在此基础上导出参数不确定线性离散混杂系统在Lyapunov意义下局部鲁棒稳定的充分条件。
(3)针对具有多个平衡点的参数不确定混杂系统，分别给出了系统可由混杂状态反馈和混杂动态输出反馈进行鲁棒镇定的充分条件，以及相应的鲁棒镇定控制器设计方法。由于控制器的设计不仅包含控制器连续时间动态行为的设计还包含离散事件动态行为的设计，因此不要求混杂系统中每个连续子系统都具有可控性或可观性。
(4)研究了含状态跳变的参数不确定混杂系统的鲁棒性能综合问题。针对积分二次型代价指标，研究了此类混杂系统的保代价控制，分别导出了系统可由混杂状态反馈和混杂动态输出反馈进行保代价控制的充分条件，提出了相应的保代价控制律设计方法，所得控制律不仅能使混杂系统对所有允许的不确定性闭环鲁棒渐近稳定，还可使系统积分二次型运行代价指标满足一定要求。针对有界幅值性能指标，研究了该类混杂系统的保性能控制问题，给出了混杂状态反馈保性能控制律的设计方法，该控制律不仅能使系统闭环鲁棒渐近稳定，还可使其闭环性能评价信号的幅值控制在给定范围之内。
11 摘 要
＊）将混杂系统保性能控制理论应用于汽车的自动变速巡航控制中，给出了
一种自动变速巡航控制汽车的保性能控制律，该控制律不仅能使汽车的巡航速度
鲁棒渐近稳定于所设定的目标值，还能将汽车的巡航加速度限制在一定的范围之
内，从而保证其乘坐的舒适性。
Hybrid systems are composed of discrete event dynamic systems and continuous time dynamic systems or discrete time dynamic systems, which interact on each other.
The hybrid system theory, which is proposed for the demand of the economic development, is the result of the development of computer science and control theory.
Hybrid systems have very complex dynamic characteristics. The performance analysis and control of hybrid systems are difficult when the parameters perturb uncertainly. Therefore, it is necessary to propose the powerful approaches for robust performance analysis and control.
Based on Lyapunov stability theory of hybrid systems and using the linear matrix inequality (LMI) method, this dissertation investigates the robust stability analysis problem, the robust stabilization problem and the robust performance synthesis problem for the linear hybrid systems with parameter uncertainties. The main contributions of this dissertation are as follows:
(1) Using the LMJ method, the problem of robust stability is discussed for the uncertain continuous hybrid systems, of which the discrete event state transition conditions are state-dependant. Based on the common Lyapunov functions, the sufficient conditions are proposed for global robust asymptotic stability. Based on the piecewise quadratic Lyapunov functions, the sufficient conditions for local robust Lyapunov stability are derived.
(2) The robust stability of uncertain linear discrete hybrid systems is investigated. The sufficient conditions for global robust asymptotic stability are proposed. Based on the multiple Lyapunov functions, the sufficient conditions are presented for local Lyapunov stability of general discrete hybrid systems. Using this result, the sufficient conditions are derived for local robust Lyapunov stability of the linear discrete hybrid sYstems with parameter perturbation.
(3) The problem of robust stabilization for uncertain hybrid systems with multiple equilibria is considered. The sufficient conditions are derived for hybrid state feedback robust stabilization and hybrid dynamic output feedback robust stabilization, respectively. The design methods of the corresponding controllers are also proposed. The controllability or the observability of the continuous time subsystems is not required since the controllers consist of the discrete event dynamics as well as the continuous time dynamics.
(4) The guaranteed cost control problem is studied for the uncertain impulsive hybrid systems and the integral quadratic cost functions. The synthesis approaches are introduced for guaranteed cost control laws via hybrid state feedback and hybrid dynamic output feedback. respectively. With the obtained control laws. the uncertain
Iv ABSTRACT
impulsive hybrid systems can be robustly asymptotically stabilized and close loop costs are guaranteed. The guaranteed performance control problem is considered for the uncertain impulsive hybrid dynamic systems and the bounded amplitude performance objectives. The method is proposed for designing the guaranteed performance control laws via hybrid state feedback. With the guaranteed performance control laws, the uncertain impulsive hybrid systems can be robustly asymptotically stabilized and the amplitudes of the performance signals can also be limited to the given range.
(5) The guaranteed performance control is applied to the vehicles with the automatic transmissions and the cruise controllers. With the guaranteed performance controller, the vehicle velocity stability and the ride comfort can be guaranteed under the uncertain conditions.
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