Stability Analysis Of Control Systems With State Saturation

Control systems with state saturation exist in the practical problems generally. It is widely used in signal processing, neural network control, etc. After adding saturated functions on the models of the control systems, it will influence greatly the original stable system and even change it into an unstable system. Therefore, it is very necessary to analyze the stability of the control systems with saturation from theoretical and practical aspects. Moreover, system parameters are inevitably disturbed by the change of internal structure and external environment. This yields the necessity to study the systems with state saturation and parameters disturbness at the same time. In this paper, stabilities and robust stabilities of control systems with state saturation are analyzed, which are organized as follows:The first problem is the stability of continuous linear state saturation system. Original methods which deal with the saturation function are improved by loosing the constraint of the additional matrix, sufficient conditions of new systems which have less conservative property and have extensively asymptotic stability at the origin are obtained, and iterative linear matrix inequality algorithms are presented. Some numerical examples are used to illustrate the effectiveness of the improved method. With the help of Matlab software, numerical simulations of the systems are presented.The second problem is robust stability of continuous linear state saturation systems with uncertain parameters. In view of norm bounded uncertainty structure satisfied by uncertain parameters, by applying Lyapunov functions and convex combination of state saturation functions, sufficient conditions, presented as linear matrix inequalities, are obtained for systems having extensively asymptotic stability at the origin. Based on this, method for designing feedback controllers is given, and an algorithm is presented to analyze robust stability of the system and to design feedback contrllers for the system. Some numerical examples are used to verify the effectiveness of the algorithm. With the help of Matlab software, the numerical simulation of the system is presented.The last problem is the stability of discrete linear systems with state saturation. By constructing an identical equation based on the difference between state values with or without state constrains, the difference of Lyapunov functions can be dealt with and sufficient conditions are presented for extensively asymptotic stability at the origin of the discrete systems, which have saturation on all states and part of the states. By comparing with existing results, it is shown that the sufficient conditions we obtain have less conservative property. Finally, some numerical examples are presented to verify the effectiveness of our results.