Author
Michał Kisielewicz
Bio: Michał Kisielewicz is an academic researcher from University of Zielona Góra. The author has contributed to research in topics: Differential inclusion & Compact space. The author has an hindex of 12, co-authored 59 publications receiving 1042 citations.
Papers published on a yearly basis
Papers
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Book•
01 Jan 1991
TL;DR: That's it, a book to wait for in this month; differential inclusions and optimal control; you may not be able to get in some stress, so don't go around and seek fro the book until you really get it.
Abstract: That's it, a book to wait for in this month. Even you have wanted for long time for releasing this book differential inclusions and optimal control; you may not be able to get in some stress. Should you go around and seek fro the book until you really get it? Are you sure? Are you that free? This condition will force you to always end up to get a book. But now, we are coming to give you excellent solution.
538 citations
Book•
12 Jun 2013
TL;DR: In this article, a list of symbols for stochastic processes is presented, including set-valued stochastic processes, set-valued stochastically intergrals, and partial differential inequalities.
Abstract: Preface.- List of Symbols.- 1. Stochastic Processes.- 2. Set-Valued Stochastic Processes.- 3. Set-Valued Stochastic Intergrals.- 4. Stochastic Differential Inclusions.- 5.Viability Theory.- 6. Partial Differential Inclusions.- 7. Some Optimal Control Problems.- Bibliography.- Subject Index.
102 citations
TL;DR: In this article, the concepts of set-valued stochastic integrals and inclusions are presented. But the main result of the paper deals with a selection property of set - valued stochastically integrals.
Abstract: We present the concepts of set - valued stochastic integrals and stochastic inclusions. The main result of the paper deals with a selection property of set - valued stochastic integrals. This property is a fundamental one for stochastic inclusions.
81 citations
TL;DR: In this article, the existence of solutions of multivalued differential equations of the form\(\dot x\)∈F(t,x), whereF is a multivalentued mapping taking as its values nonempty compact, but not necessarily convex, subsets in a separable Banach space.
Abstract: This paper is concerned with multivalued differential equations of the form\(\dot x\)∈F(t,x), whereF is a multivalued mapping taking as its values nonempty compact, but not necessarily convex, subsets in a separable Banach space. The main result is connected with the existence of solutions of these equations.
43 citations
TL;DR: In this article, the properties of the solution set of stochastic inclusions of fixed points sets of set-valued mappings are investigated and compared to properties of fixed point sets of fixed-point mappings.
Abstract: The properties of the solution set of stochastic inclusions x t − x s ∈ c l L 2 ( ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d ω τ + ∫ s t ∫ ℝ n H τ , z ( x τ ) ν ˜ ( d τ , d z ) ) are
investigated. They are equivalent to properties of fixed points sets of
appropriately defined set-valued mappings.
35 citations
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Book•
01 Jan 1994
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Abstract: Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.
11,085 citations
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.
2,446 citations
2,084 citations