Analysis And Synthesis For Classes Of Switched Systems Subject To Actuator Saturation

As an important class of hybrid systems, switched systems are of great significance both in theory development and engineering applications. Meanwhile, actuator saturation is one of the most common phenomen in practical control systems. It can degrade the performance of a control system and sometimes even lead to instability of the system. Due to the co-existence and interaction among the continuous dynamics, discrete dynamics and actuator saturation nonlinearities, the behavior of the switched systems with saturating actuators is more complicated than general switched systems or saturated systems. The mechanism of such systems is far from being clear. Many analysis and synthesis problems need to be studied. However, up to now results on such kind of switched systems have been rarely found. This dissertation studies the stabilization, the estimation of domain of attraction, L2-gain analysis and control synthesis problems for several kinds of switched systems subject to actuator saturation. The main contributions of this thesis are as follows.(1) The robust stabilization problem is addressed for a class of uncertain switched linear systems with saturating actuators. The objective is to design a switching law and the state feedback control laws such that the closed-loop system is asymptotically stable at the origin with a large domain of attraction. Via the multiple Lyapunov functions method, sufficient conditions for robust stabilization are derived. If some scalars parameters are selected in advance, the state feedback control laws and the estimation of domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints.(2) By utilizing the multiple Lyapunov functions method the L2-gain analysis and control synthesis problem is studied for a class of uncertain switched linear systems with saturating actuators. Firstly, when the controllers are pre-given, a sufficient condition is established which guarantees that the trajectories of the system with the L2disturbances are bounded. By this condition, the problem of estimating disturbance tolerance capability is formulated as a constrained optimization problem. Then, the restricted L2-gain property is analyzed over the set of tolerable disturbances. An upper bound on the restricted L2-gain is estimated by solving a constrained optimization problem. Furthermore, when controller gain matrices are design variables, these optimization problems can be adapted for controller design. All the results are presented in terms of an LMIs optimization-based approach.(3) The robust stabilization problem is investigated for a class of uncertain discrete-time switched linear systems with saturating actuators. A switching law and the state feedback laws are designed to asymptotically stabilize the system with a large domain of attraction. Based on the multiple Lyapunov functions method, sufficient conditions are obtained for robust stabilization. Furthermore, when some parameters are given in advance, the state feedback controllers and the estimation of domain of attraction are presented by solving a convex optimization problem subject to a set of LMIs constraints.(4) The problem of L2-gain analysis and control synthesis is studied for a class of uncertain discrete-time switched linear systems with time-delay and saturating actuators by using the multiple Lyapunov functions method. With the state feedback controllers adopted beforehand, a sufficient condition is derived which ensures that the closed-loop trajectories of the system remain bounded under the L2disturbances. Then with this condition, the largest disturbance tolerance level is determined via the solution of a constrained optimization problem. Then, a sufficient condition for the restricted L2-gain over the set of tolerable disturbances is derived. The smallest upper bound on the restricted L2-gain is also be obtained by solving a constrained optimization problem. Furthermore, when controller gain matrices are design variables, these optimization problems are adjusted for solving the control design task.(5) The stability analysis and anti-windup design problem is investigated for a class of uncertain discrete-time switched linear systems with saturating actuators by using the switched Lyapunov function approach. When a set of linear dynamic output controllers have been designed to stabilize the switched system without considering its input saturation, we design anti-windup compensation gains in order to enlarge the domain of attraction of the closed-loop system in the presence of saturation. Then, in terms of a sector condition, the anti-windup compensation gains are presented by solving a convex optimization problem with LMIs constraints.(6) The problem of L2-gain analysis and anti-windup compensation gains design is studied for a class of discrete-time switched systems with saturating actuators by using the switched Lyapunov function approach. For a given set of anti-windup compensation gains, we firstly give a sufficient condition which guarantees that the closed-loop trajectories of the system subject to the L2disturbances remain bounded. Then, the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances. Furthermore, the anti-windup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with LMIs constraints.Finally, the results of the dissertation are summarized and further research topics are pointed out.