On global stability of planar systems with state‐dependent Riccati equation control

Abstract

This paper is concerned with the global asymptotic stability (GAS) of a class of planar systems with a state-dependent Riccati equation (SDRE) control. Based on the philosophy of feedback domination along with the depiction of the influence arising from system nonlinearities, a sufficient condition indicating the allowable intervals of control gains is established by which the GAS of the system with SDRE control can be guaranteed successfully. The presented condition is delicately equipped with a tunable parameter skillfully enhancing the feasibility while providing a new insight and perspective in ensuring global stability of the SDRE control. A numerical example is provided to verify the effectiveness of the proposed result.

The new solution bounds of the discrete algebraic Riccati equation and their applications in redundant control inputs systems

“…The estimation of the solution bounds of the DARE has long been a heated topic [14][15][16][17][18]. And the solution bounds of the DARE can be applied in many control problems, such as the feedback controller gain in redundant optimal control [8,12], controller design [25,26], robust stability of the control systems [19][20][21], multi-agent systems [22], as well as convergence of the numerical algorithm [23,24]. So it is very meaningful to utilize the obtained upper bounds to redundant control inputs systems.…”