7 results
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2. Switched Control for Quantized Feedback Systems: Invariance and Limit Cycle Analysis.
- Author
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Papadopoulos, Alessandro Vittorio, Terraneo, Federico, Leva, Alberto, and Prandini, Maria
- Subjects
- *
FEEDBACK control system stability , *SWITCHED communication networks , *LIMIT cycles , *MATHEMATICAL symmetry , *PERIODIC functions - Abstract
We study feedback control for a discrete-time integrator with unitary delay in the presence of quantization both in the control action and in the measurement of the controlled variable. In some applications the quantization effects can be neglected, but when high precision is needed, they have to be explicitly accounted for in control design. In this paper, we propose a switched control solution for minimizing the effect of quantization of both the control and controlled variables for the considered system, that is quite common in the computing systems domain, for example, in thread scheduling, clock synchronization, and resource allocation. We show that the switched solution outperforms the one without switching, designed by neglecting quantization, and analyze necessary and sufficient conditions for the controlled system to exhibit periodic solutions in the presence of an additive constant disturbance affecting the control input. Simulation results provide evidence of the effectiveness of the approach. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
3. Analyzing the Stability of Switched Systems Using Common Zeroing-Output Systems.
- Author
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Lee, Ti-Chung, Tan, Ying, and Mareels, Iven
- Subjects
- *
SWITCHED communication networks , *TIME-varying systems , *ROBUST stability analysis , *LINEAR systems , *LYAPUNOV functions - Abstract
This paper introduces the notion of common zeroing-output systems (CZOS) to analyze the stability of switched systems. The concept of CZOS allows one to verify weak zero-state detectability. It characterizes a common behavior of any individual subsystem when the output signal for each subsystem is “approaching” zero. Heuristically speaking, it removes the effect of switching behavior, and thus enables one to analyze stability properties in systems with complex switching signals. With the help of CZOS, the Krasovskii–LaSalle theorem can be extended to switched nonlinear time-varying systems with both arbitrary switching and more general restricted switching cases. For switched nonlinear time-invariant systems, the needed detectability condition is further simplified, leading to several new stability results. Particularly, when a switched linear time-invariant system is considered, it is possible to generate a recursive method, which combines a Krasovskii–LaSalle result and a nested Matrosov result, to find a CZOS if it exists. The power of the proposed CZOS is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
4. Hybrid Model Reference Adaptive Control of Piecewise Affine Systems.
- Author
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di Bernardo, Mario, Montanaro, Umberto, and Santini, Stefania
- Subjects
- *
SWITCHING theory , *ADAPTIVE control systems , *GLOBAL asymptotic stability , *NUMERICAL analysis , *LINEAR systems , *MATHEMATICAL models - Abstract
This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for multimodal piecewise-affine (PWA) and piecewise-linear systems. The control allows the plant to track asymptotically the states of a multimodal piecewise affine (or smooth) reference model. The reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant. Numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
5. Stability and Transient Performance of Discrete-Time Piecewise Affine Systems.
- Author
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Mirzazad-Barijough, Sanam and Lee, Ji-Woong
- Subjects
- *
STRUCTURAL stability , *TRANSIENTS (Dynamics) , *DISCRETE-time systems , *PERFORMANCE evaluation , *MATHEMATICAL models , *LINEAR matrix inequalities - Abstract
This paper considers asymptotic stability and transient performance of discrete-time piecewise affine systems. We propose a procedure to construct a nested sequence of finite-state symbolic models, each of which abstracts the original piecewise affine system and leads to linear matrix inequalities for guaranteed stability and performance levels. This sequence is in the order of decreasing conservatism, and hence gives us the option to pay more computational cost and analyze a finer symbolic model within the sequence in return for less conservative results. Moreover, in the special case where this sequence is finite, an exact analysis of stability and performance is achieved via semidefinite programming. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
6. Input to State Stabilizing Controller for Systems With Coarse Quantization.
- Author
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Sharon, Yoav and Liberzon, Daniel
- Subjects
- *
STRUCTURAL stability , *QUANTIZATION (Physics) , *MEASURE theory , *PARAMETER estimation , *FEEDBACK control systems , *STRUCTURAL analysis (Engineering) , *NONLINEAR systems - Abstract
We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with quantized measurements. Quantizers considered in this paper take finitely many values and have an adjustable “center” and “zoom” parameters. Both the full state feedback and the output feedback cases are considered. Similarly to previous techniques from the literature, our proposed controller switches repeatedly between “zooming out” and “zooming in.” However, here we use two modes to implement the “zooming in” phases, which allows us to attenuate an unknown disturbance while using the minimal number of quantization regions. Our analysis is trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We further show that our method is robust to modeling errors using a specially adapted small-gain theorem. The main results are developed for linear systems, but we also discuss their extension to nonlinear systems under appropriate assumptions. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
7. Finite Time Stabilization of a Perturbed Double Integrator—Part I: Continuous Sliding Mode-Based Output Feedback Synthesis.
- Author
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Orlov, Yury, Aoustin, Yannick, and Chevallereau, Christine
- Subjects
- *
LYAPUNOV stability , *PERTURBATION theory , *SLIDING mode control , *ROBUST control , *OBSERVABILITY (Control theory) , *NUMERICAL analysis , *MULTIPLE integrals , *SIMULATION methods & models - Abstract
The twisting and supertwisting algorithms, generating important classes of second order sliding modes (SOSMs), are well-recognized for their finite time stability and robustness properties. In the present paper, a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of SOSM's that present the afore-mentioned attractive features. Thus modified, the twisting and supertwisting algorithms are utilized in the state feedback synthesis and, respectively, velocity observer design, made for the finite time stabilization of a double integrator if only output measurements are available. Performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
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