Hard problems in linear control theory: possible approaches to their solution

DOI10.1007/s10513-005-0115-0zbMath1095.93011OpenAlexW2034651194MaRDI QIDQ2487588

P. S. Shcherbakov, Boris T. Polyak

Publication date: 8 August 2005

Published in: Automation and Remote Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10513-005-0115-0

Mathematics Subject Classification ID

Feedback control (93B52) Research exposition (monographs, survey articles) pertaining to systems and control theory (93-02) Robust stability (93D09)

Related Items

Arbitrary Pole Placement by Constant Output Feedback for Linear Time Invariant Systems ⋮ On ``superstable discrete systems ⋮ On the output stabilization problem: constructing a delay feedback for a chain of integrators ⋮ Optimization of linear systems subject to bounded exogenous disturbances: the invariant ellipsoid technique ⋮ Stabilization problems for a system with output feedback (review) ⋮ Some classical number sequences in control system design ⋮ Optimization problems for periodic systems ⋮ Fixed order controller design subject to engineering specifications ⋮ On polytopes in Hurwitz region ⋮ Constructive algorithm to vectorize \((P \otimes P\) product for symmetric matrix \(P\) ⋮ Unnamed Item ⋮ Vibrational stabilization and the Brockett problem ⋮ Synthesis of simple robust controllers ⋮ Pole assignment problem for a second-order system ⋮ Stabilization of linear control systems and pole assignment problem: a survey ⋮ Stabilization of the second-order linear time-invariant control systems by a delayed feedback ⋮ Extremal pole placement in control systems with a low order controller ⋮ Identification of the position of an equilibrium attitude of the international space station as a problem of stable matrix completion ⋮ Infinite polytopes in Hurwitz stability region ⋮ Stabilisation of discrete-time systems via Schur stability region ⋮ Random search of stable member in a matrix polytope ⋮ Robust stability and evaluation of the quality functional for nonlinear control systems ⋮ Fixed-order stabilising controller design by a mixed randomised/deterministic method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability radius for structured perturbations and the algebraic Riccati equation
• Nondifferentiable optimization algorithm for designing control systems having singular value inequalities
• A Riccati equation approach to the stabilization of uncertain linear systems
• Root locations of an entire polytope of polynomials: It suffices to check the edges
• Frequency criteria of robust stability and aperiodicity of linear systems
• Several NP-hard problems arising in robust stability analysis
• Static output feedback -- a survey
• Robust analysis and design of control systems using interval arithmetic
• Robust stabilization and guaranteed cost control for discrete-time linear systems by static output feedback.
• Superstable linear control systems. I: Analysis
• Superstable linear control systems. II: Design
• Robust stability and performance with fixed-order controllers
• A formula for computation of the real stability radius
• Necessary conditions for the stability of polynomials and their use
• The \(D\)-decomposition theory
• Generalized superstability in control theory
• Structure and synthesis of PID controllers.
• Optimal design for discrete-time linear systems via new performance index
• Output Feedback and Generic Stabilizability
• Matrix Analysis
• <tex>l^{1}</tex>-optimal feedback controllers for MIMO discrete-time systems
• Multivariable Nyquist criteria, root loci, and pole placement: A geometric viewpoint
• Frequency domain criteria for l/sup p/-robust stability of continuous linear systems
• Complete instability of a box of polynomials
• Output feedback stabilization and related problems-solution via decision methods
• On pole assignment in linear multivariable systems using output feedback
• Pole assignment by gain output feedback
• On the design of single-loop single-input-output feedback control systems in the complex-frequency domain
• Optimal guaranteed cost control and filtering for uncertain linear systems
• Linear Matrix Inequalities in System and Control Theory
• NP-Hardness of Some Linear Control Design Problems
• A convex optimization approach to fixed-order controller design for disturbance rejection in SISO systems
• Pole Placement by Static Output Feedback for Generic Linear Systems
• Stochastic algorithms for exact and approximate feasibility of robust LMIs
• A New Class of Stabilizing Controllers for Uncertain Dynamical Systems
• Correspondence : Correction to ‘The zeros of a system’
• Common Lyapunov Functions and Gradient Algorithms
• Open problems in mathematical systems and control theory
• Probabilistic robust design with linear quadratic regulators