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A novel Lyapunov functional for stability of time-varying delay systems via matrix-refined-function
Automatica, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tae H Lee, Ju H Park
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Common Lyapunov function approach to matrix root clustering
Systems and Control Letters, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Takehiro Mori, Y. Mori, Hideki Kokame
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A modified matrix sign function method for projected Lyapunov equations
Systems and Control Letters, 2007The paper presents the numerical solution of a projected generalized continuous-time algebraic Lyapunov equation (GCALE): \(E^TXA+A^TXE=-P_rGP_r\). \(E, A, G\in R^{n\times n}\) are given matrices. \(X=P_1XP_1\in R^{n\times n}\) is an unknown matrix, where \(P_1\) and \(P_r\) are spectral projections onto the left and right deflating subspaces ...
Tatjana Stykel
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Nonlinear Analysis: Theory, Methods & Applications, 1984
For a system of equations \(dx/dt=f(x)\), \(f(0)=0\) where \(x\in R^ n\), \(f:N\to R^ n\), \(N\subset R^ n\) the author introduces the Lyapunov matrix-function (1) \({\mathcal B}(x)=\{w_{ij}(x)\}^ m_{i,j=1}\), \(w_{ij}(0)=0\); \(\bar {\mathcal B}(x)=\max_{i,j}w_{ij}(x)\), i,\(j\in [1,m]\) and its derivative \(\quad (2)\quad\overset \circ {\mathcal B}(x)
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For a system of equations \(dx/dt=f(x)\), \(f(0)=0\) where \(x\in R^ n\), \(f:N\to R^ n\), \(N\subset R^ n\) the author introduces the Lyapunov matrix-function (1) \({\mathcal B}(x)=\{w_{ij}(x)\}^ m_{i,j=1}\), \(w_{ij}(0)=0\); \(\bar {\mathcal B}(x)=\max_{i,j}w_{ij}(x)\), i,\(j\in [1,m]\) and its derivative \(\quad (2)\quad\overset \circ {\mathcal B}(x)
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40 Years of the Direct Matrix-Valued Lyapunov Function Method (Review)*
International Applied Mechanics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A A Martynyuk, Martynyuk A A
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The Lyapunov matrix function and the stability of hybrid systems
Soviet Applied Mechanics, 1985The purpose of the present article is to solve the problem of the stability of the equilibrium state of a hybrid (complex) system \(\Sigma\) consisting of a number of rigid, elastic, and liquid substances, related by connecting functions. The subsystems include both stable and unstable ones and the stability of the equilibrium state of the entire ...
A A Martynyuk, Martynyuk A A
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The Lyapunov matrix-function and stability of hybrid systems
Nonlinear Analysis: Theory, Methods & Applications, 1986The concept of matrix Lyapunov function (not to be confused with scalar function presented in vector-matrix form) is applied to the investigation of the stability of the isolated equilibrium state of hybrid systems. This approach allows one to universalize the procedure of construction of the appropriate Lyapunov function and to find an algorithm for ...
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2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012 This paper presents a new framework to deal with robust stability analysis for time-invariant parameter-dependent systems. It hinges upon two results: -the matrix sign function integral definition. -A particular representation of parameter-dependent matrices with negative and positive power series with respect to parameters.
Guerra, Jeremie +2 more
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Analytical construction of the hierarchical matrix Lyapunov function for impulse systems
Ukrainian Mathematical Journal, 1997 See the review in Zbl 0887.93062.
Martynyuk, A. A., Begmuratov, K. A.
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