Memoryless Linear Feedback Research Articles

A Semiglobal Approach for Stabilizing Nonlinear Systems With State Delays by Memoryless Linear Feedback

This article investigates the problem of how to control nonlinear systems with delays in the state by memoryless linear feedback. The notions of semiglobal asymptotic stabilization and sublevel sets are introduced in the context of time-delay systems. With the aid of Razumikhin theorem, we develop a semiglobal design method for the construction of Lyapunov functions, associated sublevel sets, and delay-free linear state feedback laws, step-by-step, achieving semiglobal asymptotic stabilization for time-delay nonlinear systems in a lower triangular form. In contrast to the global stabilization of nonlinear systems with delays in the state, which is usually achieved by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dynamic state</i> feedback (Lin and Zhang, 2020), the significance of this work is to point out that a tradeoff of the control objectives, e.g., semiglobal versus global stabilization, makes it possible to control a class of time-delay nonlinear systems by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">static linear</i> feedback. Extensions to nonlinear systems with globally asymptotically locally expoentially stable (GALES)-like inverse dynamics are also included in this article.

Memoryless linear feedback control for a class of upper-triangular systems with large delays in the state and input

This paper studies the problem of global asymptotic stabilization for a class of upper-triangular systems with large delays in the state and input. Using the idea of feedback domination, we develop a Lyapunov-Krasovskii method for the design of time-invariant, memoryless linear state and output feedback controllers, achieving global asymptotic stabilization of the closed-loop systems under a linear growth condition. The resulting controllers are different from predictor-based or delay-dependent controllers in the sense that they are delay-free and easier to be implemented due to the nature of “memoryless” feedback. Two examples are presented to demonstrate the effectiveness of the proposed delay-free state and output feedback control strategies.

Single-U RC integrators

This brief proves that single-pole behavior can be achieved using a single grounded uniformly distributed RC element. The transfer function generated out of a grounded UR~C~ and a memoryless linear feedback network is studied leading to two novel integrator topologies.

Memoryless stabilization of uncertain linear systems including time-varying state delays

The problem of stabilizing a class of uncertain time-delay systems via memoryless linear feedback is examined. The systems under consideration are linear systems with time-varying state delays. They also contain uncertain parameters (possibly time-varying) whose values are known only to within a prescribed compact bounding set. The main contribution given is to enlarge the class of time-delay systems for which one can construct a stabilizing memoryless linear feedback controller. Within this framework, a novel notion of robust memoryless stabilizability is first introduced via the method of Lyapunov functionals. Then a sufficient condition for the stabilizability is proposed. It is shown that solvability of a parameterized Riccati equation can be used to determine whether the time-delay system satisfies the sufficient condition. If there exists a positive definite symmetric solution satisfying the Riccati equation, a suitable memoryless linear feedback law can be derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Output feedback stabilization and related problems-solution via decision methods

Given an unstable finite-dimensional linear system, the output feedback problem is, first, to decide whether it is possible by memoryless linear feedback of the output to stabilize the system, and, second, to determine a stabilizing feedback law if such exists. This paper shows how this and a number of other linear system theory problems can be simply reformulated so as to allow application of known algorithms for solution of the existence question, with the construction problem being solved by some extension of these known algorithms. The first part of the output feedback problem is solvable with a finite number of rational operations, and the second with a finite number of polynomial factorizations. Other areas of application of the algorithm are described: Stability and positivity tests, low-order observer and controller design, and problems related to output feedback. Alternative computational procedures more or less divorced from the known algorithms are also proposed.