The Stability of the Systems with Command Saturation, Command Delay, and State Delay

This article presents the study of the stability of single-input and multiple-input systems with point or distributed state delay and input delay and input saturation. By a linear transformation applied to the initial system with delay, a system is obtained without delay, but which is equivalent from the point of view of stability. Next, using sufficient conditions for the global asymptotic stability of linear systems with bounded control, new sufficient conditions are obtained for global asymptotic stability of the initial system with state delay and input delay and input saturation. In addition, the article presents the results on the instability and estimation of the stability region of the delay and input saturation system. The numerical simulations confirming the results obtained on stability were performed in the MATLAB/Simulink environment. A method is also presented for solving a transcendental matrix equation that results from the process of equating the stability of the systems with and without delay, a method which is based on the computational intelligence, namely, the Particle Swarm Optimization (PSO) method.

Nonlinear Control System for Non-Affine Undefined Plants with Output Delays

The article deals with the problem of synthesis of the control algorithms for combined nonlinear control system for one class of single-channel non-affine priory uncertain plants with state delay in the presence of permanent bounded external noises and at measuring only the plant’s output signal. As methods for solving this problem V. M. Popov’s hyperstability criterion and the conditions of L-dissipativity are used. With the help of simulation the operation quality of the obtained system at different values of the plant relative order and its parameters is shown. The results obtained in article may be useful for construction the control systems for different dynamic plants which contains input nonlinearities and state delays.