Stability Analysis And Robust Stabilization Of Several Classes Of Linear Systems

Stability is a basic structural characteristic of a system. In most cases, stability is the premise to ensure the normal operation of the system. Therefore, it has very important theoretical and practical values to investigate the stability conditions and control law for the system.The stability analysis and robust stability for linear time-varying systems, linear discrete-time systems with time-delays and linear singular systems with time-delays is studied in this paper. The main work of this paper is as follows:1. It is discusses the stability and robust stabilization for a class of linear time-varying systems, some sufficient criteria on robust exponential stability and control methods are established. The result is less conservative than previous ways, and it is easy to be calculated.2. For a class of linear discrete-time systems with time-delays, a sufficient condition and the corresponding controller designing method which lets the closed-system to be asymptotic stability are established. The result is less conservative and lower computational complexity than previous methods, and it is easy to be calculated.3. The stability analysis and robust stability for a class of linear singular systems with time-days is studied based on time discretization and approximation theory. A sufficient condition and the corresponding controller designing method which lets the closed-system to be asymptotic stability are established. The advantage of the approach is the theory is very simple, and it is easy to be calculated.4. The problem of robust stabilization for a class of uncertain discrete singular systems with a time-varying delay is investigated. And a robust stabilization criterion for the system is proposed in terms of linear matrix inequalities. The result is less conservative than previous methods, and it is easy to be calculated.