Stabilization of Linear Control Systems and Pole Assignment Problem: A Survey

Shumafov, M. M.

doi:10.1134/s1063454119040095

Cited by 14 publications

(6 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These solutions involve either periodic scalar control gains [11], [12], [14], or some very strong conditions on the system matrix [13], which may not be satisfied in practice. A more recent review on the linear timeinvariant system stabilization problem and available solutions to output stabilization control is presented in [15]. However, a solution to the Brockett decentralized stabilization under a structural gain matrix K(t) still remains open.…”

Section: A Background and Relevant Literaturementioning

confidence: 99%

“…A more recent review on the stabilization problem and available solutions is presented in [15]. Compared to these available design solutions in [11]- [13] and more recent solutions reviewed in [15], this paper presents the first step with simple-to-verify matrix conditions that solve the Brockett stabilization problem with structured time-dependent gain matrix K(t) = diag(k i (t)) in a diagonal form.…”

Section: B Scalar/matrix Gain Conditions and Time-varying Stabilizati...mentioning

confidence: 99%

See 1 more Smart Citation

A time-varying matrix solution to the Brockett decentralized stabilization problem

Sun¹

2023

Preprint

View full text Add to dashboard Cite

This paper proposes a time-varying matrix solution to the Brockett stabilization problem. The key matrix condition shows that if the system matrix product CB is a Hurwitz H-matrix, then there exists a time-varying diagonal gain matrix K(t) such that the closed-loop minimum-phase linear system with decentralized output feedback is exponentially convergent. The proposed solution involves several analysis tools such as diagonal stabilization properties of special matrices, stability conditions of diagonal-dominant linear systems, and solution bounds of linear time-varying integro-differential systems. A review of other solutions to the general Brockett stabilization problem (for a general unstructured time-varying gain matrix K(t)) and a comparison study are also provided.

show abstract

Section: A Background and Relevant Literaturementioning

confidence: 99%

Section: B Scalar/matrix Gain Conditions and Time-varying Stabilizati...mentioning

confidence: 99%

A time-varying matrix solution to the Brockett decentralized stabilization problem

Sun¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…To avoid the above problem, a common practice for nonovershooting control is to place all the closed loop poles on the negative real axis by arbitrary pole placement technique 10 , and reader can refer to Shumafov 12 for a through survey of the pole placement control of linear systems. The disadvantage of this method is that the order of the designed systems will be very high, since arbitrary pole placement requires high order controllers be used for higher order plants 13 .…”

Section: Introductionmentioning

confidence: 99%

Design of simple nonovershooting controllers for linear high order systems with or without time delay

Du,

Feng,

Shen

et al. 2024

Sci Rep

View full text Add to dashboard Cite

In this paper, we mainly considered the problem of nonovershooting control of high order systems with or without time delay by simple controllers. As basic principles for nonovershooting control systems, three propositions are offered and proved. Under direction of these principles, a nonovershooting dominant pole control structure having three dominant poles, i.e., one real pole and a pair of complex conjugate poles on its left, is proposed. While its zeroes and nondominant poles are on the left side of these three dominant poles with sufficient distance. The controllers adopted are composed by first order filter and PD-PID controller. Dominance of the three dominant poles can be checked and ensured through the computational method we offered. Two illustrating examples are given to show the effectiveness of our method.

show abstract

“…For them, there are effective methods that provide their exact solution, provided that all components of the state vector can be used in the controller and no obvious restrictions are imposed on the choice of values of feedback coefficients. However, these problems turn out to be difficult to solve if they take into account restrictions on the structure of the controller, in particular, consisting in the prohibition of using some state variables, which occurs, for example, when synthesizing output feedback [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Pole placement with minimum gain and sparse static feedback

Sevinov,

Kadirov,

Boeva

et al. 2024

E3S Web Conf.

View full text Add to dashboard Cite

The work addresses the issue of developing polar positioning algorithms for linear control systems with despotic thinning constraints on a static feedback matrix. The design of sparse-limiting feedback control systems is considered to be one of the more complex issues, but the issue of defining the sparse feedback matrix, which allows the selection of eigenvalues or, in other words, the placement of poles, has not been fully studied. Algorithms for determining the eigenvalues, i.e., solving the problem of pole placement and finding the optimal solution of the technological process control system are considered in the work. The results of numerical analysis confirmed the effectiveness of these algorithms, which allows them to be used in solving practical problems of synthesizing adaptive control systems for technological objects.

show abstract

Stabilization of Linear Control Systems and Pole Assignment Problem: A Survey

Cited by 14 publications

References 58 publications

A time-varying matrix solution to the Brockett decentralized stabilization problem

A time-varying matrix solution to the Brockett decentralized stabilization problem

Design of simple nonovershooting controllers for linear high order systems with or without time delay

Pole placement with minimum gain and sparse static feedback

Contact Info

Product

Resources

About