Variable-structure control systems Book

	Preface	7
1	Introduction	9
1.1	Specific Problems in Discrete Stabilization	9
1.2	Discrete Dynamic Systems	14
1.3	Discrete Control Systems	18
1.4	Digital Control Systems	19
2	Mathematical Models for Digital System Control of Uncertain Plant	25
2.1	Digital Control System: Control Algorithm, Modulation, Quantization	25
2.2	Types of Hybrid Pulse Modulation	29
2.3	Discretization of Systems with Pulse-Amplitude Frequency Modulation	33
2.4	On Solvability of the Robust Stabilization Problem	43
2.5	Pulse Modelling as a Method for Generating Discrete Systems	47
3	Structural Transformations and Space Decomposition of Finite- Dimensional Dynamic Systems: Quasi-Splitting Method	49
3.1	Quasi-Splitting Method	49
3.2	Algebraic Projectors, Their Representation and Properties	60
3.3	Structural Transformations	82
3.4	Space Decomposition	95
3.5	Criteria of Invariance, Attraction and Stability for Decomposed Sets	102
3.6	Estimation of Solutions in the Class X[subscript 1]	109
4	Impulse Variable-Structure Systems	119
4.1	General Approach to the Feedback Design	119
4.2	Free Motion Control in Uncertain Systems	120
4.3	Forced Motion Control in Uncertain Systems	127
4.4	Dynamic Regulation of Discontinuous Control	132
4.5	The Study of a Digital System by Continuous Model Method	136
5	Dynamic Non-Idealities and Their Effect on the Asymptotic Behavior of Discrete Control Systems with Variable Structure	145
5.1	A Cursory Glimpse into the Theory of Discrete Control Systems with Variable Structure	146
5.2	Statement of Problem and Major Assumptions	149
5.3	Structural Transformations of Discontinuous Discrete Singularly Perturbed Systems	151
5.4	Sufficient Conditions for the Robustness of Control Systems in Terms of Global Stability	152
5.5	Enhanced Criterion for Invariance of the Sets of Cone-Type	158
5.6	The Robustness of Variable-Structure Systems Towards Small Dynamic Non-Idealities	162
6	Digital High-Gain Control Systems	169
	A Appendix : Discrete Singularly Perturbed Dynamical Systems	177
A.1	Parametrization of Perturbations	178
A.2	Continuous Singularly Perturbed Dynamical Systems	179
A.3	Discrete Singularly Perturbed Dynamical Systems in Automatic Control Problems	183
A.4	Stabilization of SPD-Systems	192
A.5	Phase Vector Estimate Control	193
A.6	Quadratic-Optimal Control of SPD-Systems	194
A.7	Robustness of Discrete Adaptive Control Systems Towards Minor Dynamical Imperfections	194
A.8	Pulse High-Gain Control Systems	195
A.9	Pulse Systems with Variable Structure	196
A.10	Parametric Identification	197
A.11	Boundary Cone-Type Layer in Discrete SPD-System Control	198
A.12	Output Measurement in Linear Feedback Systems	201
A.13	Method of Functional Relations in the Theory of Binary Control	202
A.14	Asymptotic Behavior of the Solutions of Discrete Singularity Perturbed Dynamical Systems	203
A.15	Estimation of a Small Parameter by Araki's Method	213
A.16	Time-Varying Small-Step Systems	219
A.17	Slow Motion Approximation	224
	B Appendix : Fundamentals of the Stabilization Theory of Time-Invariant Discrete Plants	235
B.1	Models	235
B.2	Statement of Control Problems	244
B.3	Stability of Motion	248
B.4	The System Properties of Discrete Linear Plants	259
B.5	Major Methods in the Design of Stabilizing Feedback	292
B.6	Problems in Discrete Stabilization Theory	310